scholarly journals Mixed lump-kink solutions and lump-soliton solutions to the generalized BKP equation with some second order terms

2021 ◽  
pp. 100254
Author(s):  
Qiao Huang ◽  
Yehui Huang ◽  
Liqin Zhang
Keyword(s):  
Soliton Solutions ◽  
Second Order ◽  
Bkp Equation

THE SECOND-ORDER KdV EQUATION AND ITS SOLITON-LIKE SOLUTION

2009 ◽  
Vol 23 (14) ◽  
pp. 1771-1780 ◽  
Author(s):  
CHUN-TE LEE ◽  
JINN-LIANG LIU ◽  
CHUN-CHE LEE ◽  
YAW-HONG KANG
Keyword(s):  
Solitary Waves ◽  
Soliton Solution ◽  
Kdv Equation ◽  
Soliton Solutions ◽  
Second Order ◽  
Close Resemblance ◽  
De Vries

This paper presents both the theoretical and numerical explanations for the existence of a two-soliton solution for a second-order Korteweg-de Vries (KdV) equation. Our results show that there exists "quasi-soliton" solutions for the equation in which solitary waves almost retain their identities in a suitable physical regime after they interact, and bear a close resemblance to the pure KdV solitons.

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

2021 ◽  
pp. 2150222
Author(s):  
Miaomiao Wang ◽  
Zequn Qi ◽  
Junchao Chen ◽  
Biao Li
Keyword(s):  
Fluid Mechanics ◽  
Soliton Solutions ◽  
Complex Interaction ◽  
Dispersive Waves ◽  
Interaction Solutions ◽  
Wave Solutions ◽  
Petviashvili Equation ◽  
Local Wave ◽  
Bkp Equation ◽  
Interaction Phenomenon

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.

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

2021 ◽  
pp. 2150388
Author(s):  
Hongcai Ma ◽  
Huaiyu Huang ◽  
Aiping Deng
Keyword(s):  
Soliton Solutions ◽  
Dynamic Graphs ◽  
Bilinear Method ◽  
Resonance Mechanism ◽  
Long Wave ◽  
Petviashvili Equation ◽  
Hybrid Solutions ◽  
Wave Limit ◽  
Bkp 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.

Multi-Soliton and Rational Solutions for the Extended Fifth-Order KdV Equation in Fluids

2015 ◽  
Vol 70 (7) ◽  
pp. 559-566 ◽  
Author(s):  
Gao-Qing Meng ◽  
Yi-Tian Gao ◽  
Da-Wei Zuo ◽  
Yu-Jia Shen ◽  
Yu-Hao Sun ◽  
...  
Keyword(s):  
Kdv Equation ◽  
Soliton Solutions ◽  
Second Order ◽  
Wave Shape ◽  
Rational Solutions ◽  
Weakly Nonlinear ◽  
First Order ◽  
Propagation Properties ◽  
Kdv Type Equations ◽  
Fifth Order

AbstractKorteweg–de Vries (KdV)-type equations are used as approximate models governing weakly nonlinear long waves in fluids, where the first-order nonlinear and dispersive terms are retained and in balance. The retained second-order terms can result in the extended fifth-order KdV equation. Through the Darboux transformation (DT), multi-soliton solutions for the extended fifth-order KdV equation with coefficient constraints are constructed. Soliton propagation properties and interactions are studied: except for the velocity, the amplitude and width of the soliton are not influenced by the coefficient of the original equation; the amplitude, velocity, and wave shape of each soltion remain unchanged after the interaction. By virtue of the generalised DT and Taylor expansion of the solutions for the corresponding Lax pair, the first- and second-order rational solutions of the equation are obtained.

scholarly journals New Exact Solutions for the (3+1)-Dimensional Generalized BKP Equation

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Jun Su ◽  
Genjiu Xu
Keyword(s):  
Exact Solutions ◽  
Evolution Equations ◽  
Soliton Solutions ◽  
Nonlinear Evolution Equations ◽  
Wronskian Technique ◽  
Rational Solutions ◽  
Wronskian Determinant ◽  
New Exact Solutions ◽  
Positon Solutions ◽  
Bkp Equation

The Wronskian technique is used to investigate a (3+1)-dimensional generalized BKP equation. Based on Hirota’s bilinear form, new exact solutions including rational solutions, soliton solutions, positon solutions, negaton solutions, and their interaction solutions are formally derived. Moreover we analyze the strangely mechanical behavior of the Wronskian determinant solutions. The study of these solutions will enrich the variety of the dynamics of the nonlinear evolution equations.

New exact optical soliton solutions for nonlinear Schrödinger equation with second-order spatio-temporal dispersion involving M-derivative

2019 ◽  
Vol 33 (20) ◽  
pp. 1950235 ◽  
Author(s):  
Behzad Ghanbari ◽  
J. F. Gómez-Aguilar
Keyword(s):  
Function Method ◽  
Velocity Dispersion ◽  
Group Velocity Dispersion ◽  
Soliton Solutions ◽  
Mathematical Physics ◽  
Second Order ◽  
Dispersion Coefficients ◽  
Nonlinear Schrödinger ◽  
Spatio Temporal ◽  
Temporal Dispersion

This paper considers the generalized nonlinear Schrödinger (GNLS) equation with group velocity dispersion and second-order spatio-temporal dispersion coefficients. We obtain new dispersive solutions of a variety of GNLS equations via the exponential rational function method with the local M-derivative of order [Formula: see text]. The results obtained demonstrate that the employed method is simple and quite efficient for constructing exact solutions for other nonlinear equations arising in mathematical physics and nonlinear optics.

scholarly journals On the optical solutions to nonlinear Schrödinger equation with second-order spatiotemporal dispersion

Open Physics ◽  
2021 ◽  
Vol 19 (1) ◽  
pp. 111-118
Author(s):  
Hadi Rezazadeh ◽  
Waleed Adel ◽  
Mostafa Eslami ◽  
Kalim U. Tariq ◽  
Seyed Mehdi Mirhosseini-Alizamini ◽  
...  
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Group Velocity Dispersion ◽  
Soliton Solutions ◽  
Expansion Method ◽  
Nonlinear Schrodinger Equation ◽  
Second Order ◽  
Wave Transformation ◽  
Nonlinear Schrödinger

Abstract In this article, the sine-Gordon expansion method is employed to find some new traveling wave solutions to the nonlinear Schrödinger equation with the coefficients of both group velocity dispersion and second-order spatiotemporal dispersion. The nonlinear model is reduced to an ordinary differential equation by introducing an intelligible wave transformation. A set of new exact solutions are observed corresponding to various parameters. These novel soliton solutions are depicted in figures, revealing the new physical behavior of the acquired solutions. The method proves its ability to provide good new approximate solutions with some applications in science. Moreover, the associated solution of the presented method can be extended to solve more complex models.

Soliton solutions for a second-order KdV equation

1994 ◽  
Vol 185 (2) ◽  
pp. 174-176 ◽  
Author(s):  
Sergei V. Korsunsky
Keyword(s):  
Kdv Equation ◽  
Soliton Solutions ◽  
Second Order
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