Short-wave Interaction System Research Articles

NOVEL INVESTIGATION OF FRACTIONAL LONG- AND SHORT-WAVE INTERACTION SYSTEM

In ocean engineering, the long- and short-wave interaction system represents a crucial nonlinear evolution equation that elucidates the resonant interaction phenomenon between ocean waves. In this study, we describe the fractional long and short-wave interaction (FLSWI) system employing the M-truncated derivative. Subsequently, we employ the extended fractional [Formula: see text] and the fractional [Formula: see text] methods to address the FLSWI system. These two approaches yields novel and intriguing soliton solutions. To further elucidate the derived soliton solutions, three-dimensional visualizations are constructed and analyzed.

Exact solutions of the stochastic fractional long–short wave interaction system with multiplicative noise in generalized elastic medium

The long–short wave interaction system (L-SWIS) is an important model describing the interaction of two waves propagating in a generalized elastic medium. In this study, the bifurcation and the influence of random interaction on the exact solution of the stochastic fractional long–short wave interaction system (SFL-SWIS) with multiplicative Brownian motion are studied, where the derivative refers to the modified Riemann–Liouville definition. After the Hamiltonian system is established by traveling wave transformation and first-order integration, we obtain abundant exact parametric solutions of SFL-SWIS. Also, the three-dimensional graph of some obtained results are drawn by using the symbolic calculation software Maple, which is used to show the influence of fractional derivative and random interaction on the solution. The obtained solitary wave solutions and exact solutions include the elliptic function solution, trigonometric function solution, exponential function solution and singular periodic solution. This study is the first to investigate the bifurcation and exact solution of SFL-SWIS, and the obtained results are theoretically and practically important to the propagation of optical signals, plasma waves and ocean waves.

Brownian motion effects on analytical solutions of a fractional-space long–short-wave interaction with conformable derivative

In this article, we consider the stochastic fractional-space long–short-wave interaction system (SFS-LSWIs) forced by multiplicative Brownian motion. To obtain a new exact stochastic fractional-space solutions, we apply two different methods such as sin–cos method and the Riccati–Bernoulli sub-ODE method. These solutions are essential for explaining some difficult and complicated physical phenomena. Because this system has never been investigated using a combination of multiplicative noise and fractional space, we will generalize certain previously obtained results as special cases. Furthermore, we use Matlab to plot 3D surfaces of analytical solutions produced in this study to show the impact of Brownian motion on the analytical solutions of the SFS-LSWIs.

The new soliton solutions for long and short-wave interaction system

The goal of this paper is to discover modern soliton solutions to long and short-wave interaction system by procedures called extended rational sine-cosine and rational sinh-cosh methods. We assume that the equation has a hypothetical soliton solutions. By reorganizing the resulting equations, we obtain a system of equations. Using Maple software, we get unknown coefficients in the system and writing them in the original equation, we obtain new solition solutions of the equation. The results show that the soliton solutions generated by the method for the long and short-wave interaction system are bright, kink type, bright periodic and dark solutions. We provided 3-D figures to illustrate the solutions. Computational results indicate that the method employed in this paper is superior than some other methods used in the literature to solve the same system equations.

Fundamental solutions for the long–short-wave interaction system

Abstract In this article, the system for the long–short-wave interaction (LS) system is considered. In order to construct some new traveling wave solutions, He’s semi-inverse method is implemented. These solutions may be applicable for some physical environments, such as physics and fluid mechanics. These new solutions show that the proposed method is easy to apply and the proposed technique is a very powerful tool to solve many other nonlinear partial differential equations in applied science.

On complex wave structures related to the nonlinear long–short wave interaction system: Analytical and numerical techniques

This article presents a survey on the exact and numerical solutions of the nonlinear long–short wave interaction system. The system performs an optical domain, which does not alter during multiplication according to a ticklish equipoise between nonlinear and linear influences in elastic surrounding (the medium that can alter the figure due to the existence of a deforming strength and comes back to its original shape in the absence of this force). The wave in this medium is obtained by vibrations that are the outcomes of the acoustic power. The modified auxiliary equation and the quintic B-spline approaches are investigated in our model to obtain a bundle of solutions to discuss new physical behaviors for this model. Moreover, the stability property is discussed for the analytical solutions via the properties related to the Hamiltonian system to show the range of the ability of solutions to be used in the applications of the model. These novel properties are explained by different types of figures. Finally, the convergence and the absolute error between the obtained solutions are discussed in a table.

Disturbance solutions for the long–short-wave interaction system using bi-random Riccati–Bernoulli sub-ODE method

This article applied the Riccati–Bernoulli (RB) sub-ODE method in order to get new exact solutions for the long–short-wave interaction (LS) equations. Namely, we obtain deterministic and random solutions, since we consider the proposed method in deterministic and random cases. The RB sub-ODE technique gives the travelling wave solutions in forms of hyperbolic, trigonometric and rational functions. It is shown that the proposed method gives a robust mathematical tool for solving nonlinear wave equations in applied science. Furthermore, some bi-random variables and some random distributions are used in random case corresponding to the LS system. The stability for the obtained solutions in random case is considered. In addition, there is a display of several numerical simulations, which helps to understand the physical phenomena of these soliton wave solutions.

Travelling Wave Solutions for the Long–Short–Wave Interaction System Using the Unified Method

The Long-Short-Wave interaction system plays a significant role between low frequency long waves and high frequency short waves. Besides being an important complex model it is also related with several physical phenomenon such as, gravity and water waves, plasma and bio-physics, nonlinear optic. This system was handled by many researchers and solutions of this system were obtained by using different methods. In this paper, new solitary type solutions for the Long-short-wave interaction system are formaly drived by using different method namely the unified method. The obtained solutions can be considered as improved version of the previous solutions. This study also shows the efficiency of the unified method.

On the classification of conservation laws and soliton solutions of the long short-wave interaction system

In this paper, the classification of conservation laws (Cls) of the long short-wave interaction system (LSWS) which appears in fluid mechanics as well as plasma physics is implemented using two Cls theorems, namely, the multipliers approach and the new conservation theorem. The LSWS describes the interaction between one long longitudinal wave and one short transverse wave propagating in a generalized elastic medium. The zeroth-order multipliers and the nonlinear self-adjoint substitutions of the model are derived. Considering the fact that the new conservation theorem needs Lie point symmetries in constructing Cls, we derive the point symmetries of a system of nonlinear partial differential equations (NPDEs) acquired by transforming the model into real and imaginary components. Moreover, we derive some kink-type, bell-shaped, singular and combined soliton solutions to the model using the powerful sine-Gordon expansion method (SGEM). Some figures are presented to show the physical interpretations of the acquired results.

On some new analytical solutions for the nonlinear long–short wave interaction system

This paper deals with exact soliton solutions of the nonlinear long–short wave interaction system, utilizing two analytical methods. The system of coupled long–short wave interaction equations is investigated with the help of two analytical methods, namely, the generalized \(\tan (\phi /2)\)-expansion method and He’s semi-inverse variational method. Moreover, in this paper we generalize two aforementioned methods which give new soliton wave solutions. As a consequence, solutions are including solitons, kink, periodic and rational solutions. Moreover, dark, bright and singular solition solutions of the coupled long–short wave interaction equations have been found. All solutions have been verified back into its corresponding equation with the aid of maple package program. We depicted the physical explanation of the extracted solutions with the free choice of the different parameters by plotting some 3D and 2D illustrations. Finally, we believe that the executed methods are robust and efficient than other methods and the obtained solutions in this paper can help us to understand the soliton waves in the fields of physics and mechanics.

On the exact solutions to the long—short-wave interaction system

The complete discrimination system for polynomial method is applied to the long—short-wave interaction system to obtain the classifications of single traveling wave solutions. Compared with the solutions given by the (G′/G)-expansion method, we gain some new solutions.

Periodic and solitary wave solutions of coupled nonlinear wave equations using the first integral method

In this paper, the periodic and solitary wave solutions of two selected systems of nonlinear wave equations are obtained using the first integral method. The long–short-wave interaction system and Bogoyavlenskii equations are considered as examples, and this approach can also be applied to other coupled nonlinear differential equations.

The periodic wave solutions for two systems of nonlinear wave equations

The periodic wave solutions for the Zakharov system of nonlinear wave equations and a long–short-wave interaction system are obtained by using the F-expansion method, which can be regarded as an overall generalization of Jacobi elliptic function expansion proposed recently. In the limit cases, the solitary wave solutions for the systems are also obtained.