Dimensional B-type Kadomtsev Petviashvili Equation Research Articles

The generalized (3 + 1)-dimensional B-type Kadomtsev–Petviashvili equation: resonant multiple soliton, N-soliton, soliton molecules and the interaction solutions

The generalized (3 + 1)-dimensional B-type Kadomtsev–Petviashvili equation: resonant multiple soliton, N-soliton, soliton molecules and the interaction solutions

Bilinear auto-Bäcklund transformations and the hybrid localized wave solutions for the ($$3+1$$)-dimensional B-type Kadomtsev–Petviashvili equation

Bilinear auto-Bäcklund transformations and the hybrid localized wave solutions for the ($$3+1$$)-dimensional B-type Kadomtsev–Petviashvili equation

Painlevé analysis, multi-kinks and hybrid nonlinear waves for an extended (3 + 1)-dimensional B-type Kadomtsev-Petviashvili equation

In this paper, we study an extended (3+1)-dimensional B-type Kadomtsev-Petviashvili equation having applications in diverse scientific fields. Painlevé anlysis is carried out to test the integrability of the model under consideration. Hirota’s simplified technique is used to investigate one, two and three kink-soliton solutions. Using a dependent variable transformation, bilinear form of the model is obtained which is then used to report lump and lump interaction solutions with periodic and kink waves. The dynamical properties and nature of obtained solutions is comprehensively studied using 3d and 2d graphs.

The symmetry breaking solutions of the nonlocal Alice–Bob B-type Kadomtsev–Petviashvili system

The (2+1)-dimensional B-type Kadomtsev–Petviashvili equation is an integrable model, which can be used to describe the shallow water wave in a fluid. In this paper, the nonlocal Alice–Bob B-type Kadomtsev–Petviashvili system is induced via the principle of PˆsxPˆsyTˆd symmetry. An extended Bäcklund transformation introduced, the symmetry breaking solution, which contains the soliton, breather, lump and their hybrid structures for this system, is solved through the Hirota bilinear form.

Nonlinear Dynamic Behaviors of the (3+1)-Dimensional B-Type Kadomtsev—Petviashvili Equation in Fluid Mechanics

This paper provides an investigation on nonlinear dynamic behaviors of the (3+1)-dimensional B-type Kadomtsev—Petviashvili equation, which is used to model the propagation of weakly dispersive waves in a fluid. With the help of the Cole—Hopf transform, the Hirota bilinear equation is established, then the symbolic computation with the ansatz function schemes is employed to search for the diverse exact solutions. Some new results such as the multi-wave complexiton, multi-wave, and periodic lump solutions are found. Furthermore, the abundant traveling wave solutions such as the dark wave, bright-dark wave, and singular periodic wave solutions are also constructed by applying the sub-equation method. Finally, the nonlinear dynamic behaviors of the solutions are presented through the 3-D plots, 2-D contours, and 2-D curves and their corresponding physical characteristics are also elaborated. To our knowledge, the obtained solutions in this work are all new, which are not reported elsewhere. The methods applied in this study can be used to investigate the other PDEs arising in physics.

Pfaffian, soliton, hybrid and periodic-wave solutions for a ($$3+1$$)-dimensional B-type Kadomtsev–Petviashvili equation in fluid mechanics

Pfaffian, soliton, hybrid and periodic-wave solutions for a ($$3+1$$)-dimensional B-type Kadomtsev–Petviashvili equation in fluid mechanics

Variable separation solution and multi-valued soliton of an extended (3+1)-dimensional B-type Kadomtsev–Petviashvili equation

Variable separation solution and multi-valued soliton of an extended (3+1)-dimensional B-type Kadomtsev–Petviashvili equation

Localized excitation and folded solitary wave for an extended (3+1)-dimensional B-type Kadomtsev–Petviashvili equation

Localized excitation and folded solitary wave for an extended (3+1)-dimensional B-type Kadomtsev–Petviashvili equation

Similarity reductions for a generalized (3+1)-dimensional variable-coefficient B-type Kadomtsev–Petviashvili equation in fluid dynamics

Rather intriguing, the paper Chin. J. Phys. 73 (2021) 600-612 has studied a (3+1)-dimensional B-type Kadomtsev–Petviashvili equation in fluid dynamics, while fluid dynamics has a wide range of applications, including those for geophysics, mechanical engineering, civil engineering, chemical engineering, astrophysics and biology. In this paper, taking into consideration certain nonlinear waves in fluid dynamics, we investigate a generalized variable-coefficient version of the aforementioned equation. Making use of symbolic computation, with respect to the amplitude or elevation of the relevant wave, we construct out two sets of the similarity reductions, which rely on the variable coefficients in the generalized equation.

Multiple breathers and high-order rational solutions of the (3+1)-dimensional B-type Kadomtsev–Petviashvili equation

This paper is devoted to obtaining the multi-soliton solutions, high-order breather solutions and high-order rational solutions of the (3+1)-dimensional B-type Kadomtsev–Petviashvili (BKP) equation by applying the Hirota bilinear method and the long-wave limit approach. Moreover, the interaction solutions are constructed by choosing appropriate value of parameters, which consist of four waves for lumps, breathers, rouges and solitons. Some dynamical characteristics for the obtained exact solutions are illustrated using figures.

Multiwave interaction solutions for a (3 + 1)-dimensional B-type Kadomtsev–Petviashvili equation in fluid dynamics

Abstract In this paper, a (3 + 1)-dimensional B-type Kadomtsev–Petviashvili (BKP) equation is investigated and its various new interaction solutions among solitons, rational waves and periodic waves are obtained by the direct algebraic method, together with the inheritance solving technique. The results are fantastic interaction phenomena, and are shown by figures. Meanwhile, any higher order interaction solutions among solitons, breathers, and lump waves are constructed by an N-soliton decomposition algorithm developed by us. These innovative results greatly enrich the structure of the solutions of this equation.

Resonance Y-shaped soliton and interaction solutions in the (2 + 1)-dimensional B-type Kadomtsev–Petviashvili equation

The ([Formula: see text])-dimensional B-type Kadomtsev–Petviashvili (BKP) equation is utilized to depict weakly dispersive waves propagating in the fluid mechanics. According to [Formula: see text]-soliton solutions, resonance Y-shaped soliton and its interaction with other local wave solutions of the ([Formula: see text])-dimensional BKP equation are derived by introducing the constraint conditions. These types of hybrid soliton solutions exhibit the complex interaction phenomenon among resonance Y-shaped solitons, breather waves, line solitary waves and high-order lump waves. The dynamic behaviors of such interaction solutions are analyzed and illustrated.

Bäcklund transformations, kink soliton, breather- and travelling-wave solutions for a (3+1)-dimensional B-type Kadomtsev–Petviashvili equation in fluid dynamics

In this paper, we investigate a (3+1)-dimensional B-type Kadomtsev–Petviashvili (BKP) equation in fluid dynamics. Based on the Hirota method, we give a bilinear auto-Bäcklund transformation. Via the truncated Painlevé expansion, we get a Painlevé-type auto-Bäcklund transformation. With the aid of the symbolic computation, we derive some one- and two-kink soliton solutions. We present the oblique and parallel elastic interactions between the two-kink solitons. Via the extended homoclinic test technique, we construct some breather-wave solutions. Besides, we derive some lump solutions with the periods of the breather-wave solutions to the infinity. We observe that the shapes of a breather wave and a lump remain unchanged during the propagation. Based on the polynomial-expansion method, travelling-wave solutions are constructed.

Soliton molecules and some novel hybrid solutions for (3+1)-dimensional B-type Kadomtsev–Petviashvili equation

In recent years, soliton molecules have received reinvigorating scientific interests in physics and other fields. Soliton molecules have been successfully found in optical experiments. In this paper, we attribute the solutions of the (3+1)-dimensional B-type Kadomtsev–Petviashvili (BKP) equation by employing the bilinear method. Based on the [Formula: see text]-soliton solutions, we establish the soliton molecules, asymmetric solitons and some novel hybrid solutions of this equation by means of the velocity resonance mechanism and the long wave limit method. Finally, we give dynamic graphs of soliton molecules, asymmetric solitons and some novel hybrid solutions.

Stripe solitons and lump solutions to a generalized (3 + 1)-dimensional B-type Kadomtsev-Petviashvili equation with variable coefficients in fluid dynamics

Under investigation is a generalized (3+1)-dimensional B-type Kadomtsev-Petviashvili equation with variable coefficients in fluid dynamics. Based on the Hirota's bilinear form and the positive quadratic function, abundant lump solutions are obtained. The interaction solutions between lump solutions and other solitons are also presented. Their dynamical behaviors are graphically shown with different choices of the free parameters.

Dynamics of abundant solutions to the generalized (3+1)-dimensional B-type Kadomtsev–Petviashvili equation

The present paper is devoted to discussion of (3+1)-dimensional generalized B-type Kadomtsev–Petviashvili (gBKP) equation from point of view of their multi-soliton solutions and localized solutions associated with multi-soliton solutions. Firstly, taking advantage of the Bell-polynomial approach, we construct the Hirota bilinear form of (1.1). Based on that, the multi-soliton solutions are also singled out. Subsequently, the (3+1)-dimensional gBKP equation is also found to allow fruitful localized solutions, including breather, lump, rogue wave, and hybrid solutions. These results obtained in this work adequately illustrate the effectiveness of the long wave limit method and complex conjugate technique, which are expected to be employed to obtain more abundant exact solutions.

An useful procedure for finding exact solutions to new form of (2 + 1)-dimensional B-type Kadomtsev–Petviashvili (BKP) equation

Existence of trigonometric and hyperbolic function solutions together yields complexiton solutions. This condition is the nature of complexitons, makes the process harder and provides them a different type of wave speed. Modified double sub-equation method is a useful and practical tool to obtain complexiton solutions of nonlinear partial differential equations. Employment of two wave transformations makes modified double sub-equation method more general than methods that use one wave transformation. These two wave transformations also provide trigonometric function solutions or hyperbolic function solutions. In this study, application of modified double sub-equation method for new form of (2 + 1)-dimensional BKP equation is given. Wave propagations of some resulting solutions are illustrated.

On the Exact Solutions of Two (3+1)-Dimensional Nonlinear Differential Equations

In this article, exact solutions of two (3+1)-dimensional nonlinear differential equations are derived by using the complex method. We change the (3+1)-dimensional B-type Kadomtsev-Petviashvili (BKP) equation and generalized shallow water (gSW) equation into the complex differential equations by applying traveling wave transform and show that meromorphic solutions of these complex differential equations belong to class W, and then, we get exact solutions of these two (3+1)-dimensional equations.

Solitary wave solutions, lump solutions and interactional solutions to the (3 + 1)-dimensional generalized B-type Kadomtsev-Petviashvili equation

In this paper, we investigate a [Formula: see text]-dimensional B-type Kadomtsev-Petviashvili (BKP) equation, which is a generalization of the [Formula: see text]-dimensional equation. Based on the Hirota bilinear method and the limit technique of long wave, we systematically construct a family of exact solutions of BKP equation including the [Formula: see text]-solitary wave solution, lump solution as well as interaction solution between lump waves and solitary waves.

Soliton molecules and some novel interaction solutions to the (2+1)-dimensional B-type Kadomtsev–Petviashvili equation

Soliton molecules may exists in both experimental and theotetical aspects. In this work, we investigate the (2+1)-dimensional B-type Kadomtsev–Petviashvili equation, which can be used to describe weakly dispersive waves propagating in the quasi media and fluid mechanics. Soliton molecules are generated by N-soliton solution and a new velocity resonance condition. Furthermore, soliton molecules can become to asymmetric solitons when the distance between two solitons of the molecule is small enough. Based on the N-soliton solution, we obtain some novel interaction solutions which component of soliton molecules, breather waves and lump waves by deal with part of parameters by applying velocity resonance, module resonance and long wave limit method, and the interactions are elastic. Finally, some graphic analysis are discussed to understand the propagation phenomena of these solutions.