Konno-Oono Equation Research Articles

Numerical treatment of the KP–MEW equation and the Konno–Oono equation using the first-integral method

Finding new, more widely applicable accurate traveling wave solutions to nonlinear partial differential equations is the aim of this work. The Konno–Oono equation and the Kadomtsev–Petviashvili modified equal width equation have various possible applications in mathematical physics and engineering disciplines, and their exact solutions are presented in this article. Using the first integral approach as an analytical method and the traveling wave transformation, we explore the precise traveling wave solutions. This approach is effective and yields unique exact solutions that fall into two categories: solutions in the form of trigonometric functions and solutions in the form of hyperbolic functions. Furthermore, graphical illustrations in two and three dimensions are showcased to offer a thorough explanation of their dynamic nature. In addition, it is critical to emphasize the significance of mastering the Konno–Oono equation and the KP–MEW equation, both of which have applications in a variety of fields Our findings are also crucial for understanding the many oceanographic applications that involve ocean gravity waves, offshore rigs in the water, energy from moving ocean waves, and several other related phenomena. This approach requires less computing work and is straightforward and succinct. That is its main advantage.

Riccati–Bernoulli sub-ode method-based exact solution of new coupled Konno–Oono equation

Nonlinear partial differential equations (NLPDEs) have emerged as a major focus of study in a variety of nonlinear science disciplines. This is because in general, mathematical, physics and engineering problems may be stated by NLPDEs. It may be noted that a specific kind of exact/analytical solution called traveling wave solutions for NLPDEs has great significance. In this regard, this paper addresses the traveling wave solution to the new coupled Konno–Oono equation (NCKOE), a set of NLPDE. A traveling wave transformation and the Riccati–Bernoulli sub-ode method (RBSOM) are used here to retrieve the exact/analytical traveling wave solution of the NCKOE. By using the above-mentioned approach, NLPDEs can be updated toward a collection of algebraic equations. Further, different types of solitary wave solitons, Trigonometric function solutions, Hyperbolic soliton solutions and dark bright solitons to the NCKOE have been successfully retrieved. Importantly, the newly derived solutions adhere to the main equation when they are inserted into the governing equations. Furthermore, through an appropriate selection of parameters, three-dimensional and two-dimensional figures are presented for physical illustration of the obtained solutions. These visual representations serve to showcase the effectiveness, conciseness and efficiency of the applied techniques.

A comprehensive study of the conformable time-fractional coupled Konno–Oono equation: new methodologies and stability analysis in magnetic field

A comprehensive study of the conformable time-fractional coupled Konno–Oono equation: new methodologies and stability analysis in magnetic field

Bifurcation, chaotic behavior, and traveling wave solution of stochastic coupled Konno–Oono equation with multiplicative noise in the Stratonovich sense

Abstract The main aim of this article is to focus on the dynamics and traveling wave solution of stochastic coupled Konno–Oono equation with multiplicative noise in the Stratonovich sense. First, the considered model is converted to the nonlinear ordinary differential equations by using traveling wave transformation. Secondly, two-dimensional phase portrait of the nonlinear ordinary differential equation and its periodic perturbation system are drawn by using Maple software. Finally, the traveling wave solutions of the investigated equation are obtained via the planar dynamic system method. Moreover, three-dimensional graphs of some obtained solutions are drawn.

Exact solutions for new coupled Konno–Oono equation via Sardar subequation method

Exact solutions for new coupled Konno–Oono equation via Sardar subequation method

Dynamical Behaviour of Conformable Time-Fractional Coupled Konno-Oono Equation in Magnetic Field

Our aim is to construct distinct types of novel traveling wave solutions for the nonlinear conformable time-fractional coupled Konno–Oono equation in a magnetic field utilizing the qualitative analysis of the dynamical system that corresponds to the Hamiltonian system. The influences of fractional-order derivative on the wave solutions in addition to equation parameters on the waveform are investigated. Furthermore, He’s variational technique has been applied to seek some new solutions. 2D and 3D graphics of the obtained solutions are presented to clarify the physical and mathematical meaning of the waves.

Study on abundant analytical solutions of the new coupled Konno–Oono equation in the magnetic field

Abstract In this article, we focus on investigating the new coupled Konno–Oono equation that arises in the magnetic field. An effective technology called the Exp-function method (EFM) is utilized to find abundant analytical solutions. By this method, four families (28 sets) of the exact solutions, such as bright solitary, dark solitary, bright–dark solitary, double-bright solitary, double-dark solitary and kinky bright–dark solitary wave solutions, are constructed. The performances of the real, imaginary and absolute parts of the solutions are presented in the form of 3D contours. The results show that the EFM is a promising method to construct abundant analytical solutions for the partial differential equations arising in physics.

Abundant analytical solutions to the new coupled Konno-Oono equation arising in magnetic field

This paper focuses on the coupled Konno-Oono equation that arises in the magnetic field. Fifteen sets of the analytical solutions in the form of bright solitary, dark solitary, bright-dark solitary, kinky bright-dark solitary, rough bright solitary and periodic wave solutions are obtained by applying three effective technologies, which are simplified extended tanh-function method, variational direct method and He’s frequency formulation. The behaviors of the solutions are plotted through the 3-D contours. The results show that the proposed methods are effective and powerful, which are expected to helpful for the study of the traveling wave theory in physics.

Closed-form solutions to the new coupled Konno–Oono equation and the Kaup–Newell model equation in magnetic field with novel statistic application

This paper employs the new robust solver to retrieve exact solutions to a Kaup–Newell model equation and the nonlinear coupled Konno–Oono equation. This solver yields the closed formula for the solutions. Different types of travelling wave solutions, i.e., rational function, hyperbolic function and trigonometric function solutions with many capricious parameters are revealed. Subsequently, by utilizing Matlab 18 we plot 2D and 3D surfaces of obtained analytical solutions for suitable values of the free parameters. The depiction of the solver is direct, vital, sturdy and can be applied to other nonlinear partial differential equations. We also show that some proposed rational solutions can be rapprochement with some known probability distributions.

Exact solutions of the stochastic new coupled Konno-Oono equation

In this paper we consider the stochastic Konno-Oono equation, which is forced by multiplicative noise. In order to find exact solutions of stochastic nonlinear Konno-Oono equations, generalized G′G-expansion method are implemented. Different forms of traveling wave solutions such as complex hyperbolic function and complex trigonometric function have emerged with various parameters. The results obtained in this paper extend and improve some results that were previously obtained. Moreover, we plot 3D surfaces of analytical solutions obtained in this paper by using Matlab to illustrate the impact of multiplicative noise on the solutions of the Konno-Oono equation.

Solitary Wave Solutions of the Coupled Konno-Oono Equation by using the Functional Variable Method and the Two Variables (G'/G,1/G) -Expansion Method

In this work, we investigate solitary wave solutions of the coupled Konno-Oono equation with the aid of the functional variable method (FVM) and the two variables (G'/G,1/G)-expansion method. We obtain solitary wave solutions in form of trigonometric function and hyperbolic function and rational function solutions. We also draw two and three-dimensional graphics for some solutions with help of Mathematica 7.

Fundamental solutions for the new coupled Konno-Oono equation in magnetic field

We implement an efficient solver to retrieve solutions to the nonlinear new coupled Konno–Oono (CKO) equation. This solver presents the closed form of solutions. Distinct types of travelling wave solutions are revealed, for example solitary wave, dark solitons, bright solitons, combined dark–bright and periodic solitary wave solutions. These solutions can be applicable in the magnetic field. Thereafter, by utilizing Matlab 18, we present 2D and 3D figures of some acquired solutions for convenient values of the parameters. The proposed technique is direct, robust, efficacious to achieve new solutions for nonlinear partial differential equations in applied science.

New closed form solutions of the new coupled Konno–Oono equation using the new extended direct algebraic method

In this paper, we apply the new extended direct algebraic method (NEDAM) to solve new exact solutions of the new coupled Konno–Oono (CKO) equation, and construct exact solution expressed in terms of hyperbolic functions and trigonometric functions with arbitrary parameters. A comparison between our established results and the results obtained by the existing ones is also presented. As a newly developed mathematical tool, the proposed method is an effective and straightforward technique to work out new solutions of various types of nonlinear partial differential equations (NLPDEs) in applied sciences and engineering.

Darboux transformation and soliton solution for generalized Konno-Oono equation

In this paper, the generalized Konno-Oono equation is investigated. Using the Lax pair, we obtain a new Darboux transformation for the dispersionless equation. A soliton solution of the generalized Konno-Oono equation is obtained on the basis of the Darboux transformation. Corresponding graphs are also built.

Dispersionless limit of the Konno-Oono equation

Dispersionless limit of the Konno-Oono equation

Multiple Soliton Solutions of Some Nonlinear Partial Differential Equations

In this paper, we implemented an improved tanh function Method for multiple soliton solutions of new coupled Konno-Oono equation and extended (3+1)-dimensional KdV-type equation.

Modified extended exp-function method for a system of nonlinear partial differential equations defined by seismic sea waves

Nonlinear partial differential equations are the main area of focus for researchers and scientists doing research in applied mathematics. Finding solutions of these nonlinear partial differential equations had gained considerable importance over the last few decades. In this work, an analytical technique named extended exp-function method is introduced for finding archetype exact solutions of innovative nonlinear coupled Konno–Oono equation. Different types of travelling wave solutions, i.e. complex hyperbolic function and complex trigonometric function solutions, with numerous capricious parameters are revealed. Subsequently, by using Maple 16, we plot 2D and 3D surfaces of analytical solutions obtained in this article. The depiction of the technique is straight, useful and can be applied to other nonlinear systems of partial differential equations.

On some new analytical solutions for new coupled Konno–Oono equation by the external trial equation method

In this paper, the external trial equation method is employed to solve new coupled Konno–Oono (CKO) equation. By using this method, new exact solutions involving parameters, expressed by generalized hyperbolic and elleptic solutions are obtained. The current method presents a wider applicability for handling nonlinear wave equations. In addition, explicit new exact solutions are derived in different form such as dark solitons, bright solitons, solitary wave, periodic solitary wave, rational function, and elliptic function solutions of CKO equation. The movements of obtained solutions are shown graphically, which helps to understand the physical phenomena of this soliton wave equation.

The new exact solutions of the new coupled Konno-Oono equation by using extended simplest equation method

The new exact solutions of the new coupled Konno-Oono equation by using extended simplest equation method

Dispersive solitary wave solutions of new coupled Konno-Oono, Higgs field and Maccari equations and their applications

In this research we apply generalized Exp-Function method to obtain exact, solitary and new soliton wave solutions of new coupled Konno-Oono equation, Higgs field equation and Maccari equation via generalized Exp-Function method which are very substantial models in define a current-fed string interacting with an external magnetic field in three-dimensional Euclidean space, introduces quantum field (or the Higgs field) to illustrate the generation mechanism of mass for gauge bosons and described the motion of the isolated waves, localized in a small part of space, in many fields such as hydrodynamic, plasma physics, nonlinear optics and others. generalized Exp-Function method is very sturdy, fabulous, felicitous and effective method to get exact, solitary and new soliton wave solution of nonlinear partial differential equations (PDEs.). We present a contrasting between the results of this modern method and another method and show that how the results that obtained by this method is much closed to cover many different methods in this field and not just that but also get a new solitary and soliton wave solutions which give a wide range of solutions that help all researchers who apply these models in our life.