scholarly journals Soliton solutions and periodic solutions for two models arises in mathematical physics

2021 ◽  
Vol 7 (3) ◽  
pp. 4439-4458
Author(s):  
F. A. Mohammed ◽  
◽  
Mohammed K. Elboree ◽  
Keyword(s):  
Soliton Solutions ◽  
Higgs Field ◽  
Periodic Wave ◽  
Jacobi Elliptic Function ◽  
Mathematical Methods ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Kudryashov Method ◽  
Kink Wave ◽  
Cubic Nonlinear Schrödinger Equation

<abstract><p>We aimed in this paper to acquire the periodic wave solutions and soliton solutions and other solutions such as kink-wave solutions for the cubic nonlinear Schrödinger equation with repulsive delta potential ($ \delta $-NLSE) and complex coupled Higgs field equation via two mathematical methods Jacobi elliptic function method and generalized Kudryashov method. Some of these solutions are degenerated to solitary wave solutions and periodic wave solutions in the limit case. We also gave the meaning of these solutions physically and the numerical simulation by some figures.</p></abstract>

EXACT TRAVELING WAVE SOLUTIONS OF A HIGHER-DIMENSIONAL NONLINEAR EVOLUTION EQUATION

2010 ◽  
Vol 24 (10) ◽  
pp. 1011-1021 ◽  
Author(s):  
JONU LEE ◽  
RATHINASAMY SAKTHIVEL ◽  
LUWAI WAZZAN
Keyword(s):  
Traveling Wave ◽  
Function Method ◽  
Soliton Solutions ◽  
Traveling Wave Solutions ◽  
Periodic Wave ◽  
Jacobi Elliptic Function ◽  
Periodic Wave Solutions ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions ◽  
Higher Dimensional

The exact traveling wave solutions of (4 + 1)-dimensional nonlinear Fokas equation is obtained by using three distinct methods with symbolic computation. The modified tanh–coth method is implemented to obtain single soliton solutions whereas the extended Jacobi elliptic function method is applied to derive doubly periodic wave solutions for this higher-dimensional integrable equation. The Exp-function method gives generalized wave solutions with some free parameters. It is shown that soliton solutions and triangular solutions can be established as the limits of the Jacobi doubly periodic wave solutions.

Solitary and periodic wave solutions of the Majda–Biello system

2016 ◽  
Vol 30 (15) ◽  
pp. 1650237 ◽  
Author(s):  
Abdullahi Rashid Adem
Keyword(s):  
Exact Solutions ◽  
Rossby Waves ◽  
Periodic Wave ◽  
Jacobi Elliptic Function ◽  
Solitary Wave Solutions ◽  
Long Wavelength ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Kudryashov Method ◽  
Equatorial Rossby Waves

In this paper, we present the exact solutions of the Majda–Biello system. This system describes the nonlinear interaction of long-wavelength equatorial Rossby waves and barotropic Rossby waves with a substantial midlatitude projection, in the presence of suitable horizontally and vertically sheared zonal mean flows. The methods used to construct the exact solutions are the Kudryashov method and Jacobi elliptic function method. These two methods yield solitary wave solutions and periodic wave solutions.

A Variety of Exact Periodic Wave and Solitary Wave Solutions for the Coupled Higgs Equation

2012 ◽  
Vol 67 (10-11) ◽  
pp. 545-549 ◽  
Author(s):  
Houria Trikia ◽  
Abdul-Majid Wazwazb
Keyword(s):  
Solitary Wave ◽  
Soliton Solutions ◽  
Higgs Field ◽  
Periodic Wave ◽  
Travelling Wave ◽  
Jacobi Elliptic Function ◽  
Travelling Wave Solutions ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Jacobi Elliptic Function Expansion

In this work, the coupled Higgs field equation is studied. The extended Jacobi elliptic function expansion methods are efficiently employed to construct the exact periodic solutions of this model. As a result, many exact travelling wave solutions are obtained which include new shock wave solutions or kink-shaped soliton solutions, solitary wave solutions or bell-shaped soliton solutions, and combined solitary wave solutions are formally obtained.

scholarly journals Periodic Wave Solutions and Their Limits for the Generalized KP-BBM Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-25 ◽  
Author(s):  
Ming Song ◽  
Zhengrong Liu
Keyword(s):  
Dynamical Systems ◽  
Solitary Wave ◽  
Blow Up ◽  
Periodic Wave ◽  
Solitary Wave Solutions ◽  
Bifurcation Method ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Kink Wave ◽  
Bbm Equation

We use the bifurcation method of dynamical systems to study the periodic wave solutions and their limits for the generalized KP-BBM equation. A number of explicit periodic wave solutions are obtained. These solutions contain smooth periodic wave solutions and periodic blow-up solutions. Their limits contain periodic wave solutions, kink wave solutions, unbounded wave solutions, blow-up wave solutions, and solitary wave solutions.

Resonance Y-type soliton, hybrid and quasi-periodic wave solutions of a generalized (2+1)-dimensional nonlinear wave equation

2021 ◽  
Author(s):  
Lingchao He ◽  
Jianwen Zhang ◽  
Zhonglong Zhao
Keyword(s):  
Wave Equation ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Water Waves ◽  
Asymptotic Properties ◽  
Soliton Solutions ◽  
Periodic Wave ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Before And After

Abstract In this paper, we consider a generalized (2+1)-dimensional nonlinear wave equation. Based on the bilinear, the N-soliton solutions are obtained. The resonance Y-type soliton and the interaction solutions between M-resonance Y-type solitons and P-resonance Y-type solitons are constructed by adding some new constraints to the parameters of the N-soliton solutions. The new type of two-opening resonance Y-type soliton solutions are presented by choosing some appropriate parameters in 3-soliton solutions. The hybrid solutions consisting of resonance Y-type solitons, breathers and lumps are investigated. The trajectories of the lump waves before and after the collision with the Y-type solitons are analyzed from the perspective of mathematical mechanism. Furthermore, the multi-dimensional Riemann-theta function is employed to investigate the quasi-periodic wave solutions. The one-periodic and two-periodic wave solutions are obtained. The asymptotic properties are systematically analyzed, which establish the relations between the quasi-periodic wave solutions and the soliton solutions. The results may be helpful to provide some effective information to analyze the dynamical behaviors of solitons, fluid mechanics, shallow water waves and optical solitons.

Nonlocal Symmetry and Consistent Tanh Expansion Method for the Coupled Integrable Dispersionless Equation

2016 ◽  
Vol 71 (3) ◽  
pp. 235-240 ◽  
Author(s):  
Hengchun Hu ◽  
Xiao Hu ◽  
Bao-Feng Feng
Keyword(s):  
Soliton Solutions ◽  
Expansion Method ◽  
Periodic Wave ◽  
Cnoidal Wave ◽  
Nonlocal Symmetry ◽  
Nonlocal Symmetries ◽  
Periodic Wave Solutions ◽  
Wave Solutions

AbstractNonlocal symmetries are obtained for the coupled integrable dispersionless (CID) equation. The CID equation is proved to be consistent, tanh-expansion solvable. New, exact interaction excitations such as soliton–cnoidal wave solutions, soliton–periodic wave solutions, and multiple resonant soliton solutions are discussed analytically and shown graphically.

BIFURCATIONS AND EXACT TRAVELING WAVE SOLUTIONS OF THE GENERALIZED TWO-COMPONENT CAMASSA–HOLM EQUATION

2012 ◽  
Vol 22 (12) ◽  
pp. 1250305 ◽  
Author(s):  
JIBIN LI ◽  
ZHIJUN QIAO
Keyword(s):  
Solitary Wave ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Periodic Wave ◽  
Breaking Wave ◽  
Solitary Wave Solutions ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Two Component ◽  
Kink Wave

In this paper, we apply the method of dynamical systems to a generalized two-component Camassa–Holm system. Through analysis, we obtain solitary wave solutions, kink and anti-kink wave solutions, cusp wave solutions, breaking wave solutions, and smooth and nonsmooth periodic wave solutions. To guarantee the existence of these solutions, we give constraint conditions among the parameters associated with the generalized Camassa–Holm system. Choosing some special parameters, we obtain exact parametric representations of the traveling wave solutions.

EXACT SOLITON SOLUTIONS AND QUASI-PERIODIC WAVE SOLUTIONS TO THE FORCED VARIABLE-COEFFICIENT KdV EQUATION

2012 ◽  
Vol 26 (19) ◽  
pp. 1250072 ◽  
Author(s):  
YI ZHANG ◽  
ZHILONG CHENG
Keyword(s):  
Variable Coefficient ◽  
Kdv Equation ◽  
Soliton Solutions ◽  
Periodic Wave ◽  
Time Dependent ◽  
Bilinear Method ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Hirota Bilinear ◽  
Exact Soliton Solutions

In this paper, the time-dependent variable-coefficient KdV equation with a forcing term is considered. Based on the Hirota bilinear method, the bilinear form of this equation is obtained, and the multi-soliton solutions are studied. Then the periodic wave solutions are obtained by using Riemann theta function, and it is also shown that classical soliton solutions can be reduced from the periodic wave solutions.

TRAVELING WAVES FOR AN INTEGRABLE HIGHER ORDER KDV TYPE WAVE EQUATIONS

2006 ◽  
Vol 16 (08) ◽  
pp. 2235-2260 ◽  
Author(s):  
JIBIN LI ◽  
JIANHONG WU ◽  
HUAIPING ZHU
Keyword(s):  
Solitary Wave ◽  
Wave Equations ◽  
Sufficient Conditions ◽  
Periodic Wave ◽  
Higher Order ◽  
Solitary Wave Solutions ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Kink Wave ◽  
Planar Dynamical Systems

Using the method of planar dynamical systems to a higher order wave equations of KdV type, the existence of smooth and nonsmooth solitary wave, kink wave and uncountably infinite many periodic wave solutions is proved. In different regions of the parametric space, the sufficient conditions to guarantee the existence of the above solutions are given. In some spatial conditions, the exact explicit parametric representations of solitary wave solutions are determined.

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