scholarly journals Topological and Non-Topological Soliton Solutions of the Coupled Klein-Gordon-Schrodinger and the Coupled Quadratic Nonlinear Equations

2014 ◽  
Vol 3 (1) ◽  
pp. 1-5 ◽  
Author(s):  
Mozhgan Akbari
Keyword(s):  
Nonlinear Equations ◽  
Soliton Solutions ◽  
Topological Soliton ◽  
Klein Gordon

scholarly journals Topological Soliton Solution and Bifurcation Analysis of the Klein-Gordon-Zakharov Equation in(1+1)-Dimensions with Power Law Nonlinearity

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Ming Song ◽  
Bouthina S. Ahmed ◽  
Anjan Biswas
Keyword(s):  
Finite Difference ◽  
Numerical Simulations ◽  
Power Law ◽  
Soliton Solution ◽  
Bifurcation Analysis ◽  
Soliton Solutions ◽  
Phase Portraits ◽  
Zakharov Equation ◽  
Topological Soliton ◽  
Klein Gordon

This paper addresses the Klein-Gordon-Zakharov equation with power law nonlinearity in (1+1)-dimensions. The integrability aspect as well as the bifurcation analysis is studied in this paper. The numerical simulations are also given where the finite difference approach was utilized. There are a few constraint conditions that naturally evolve during the course of derivation of the soliton solutions. These constraint conditions must remain valid in order for the soliton solution to exist. For the bifurcation analysis, the phase portraits are also given.

scholarly journals Onset of the broad-ranging general stable soliton solutions of nonlinear equations in physics and gas dynamics

2021 ◽  
Vol 20 ◽  
pp. 103762
Author(s):  
Md. Abdul Kayum ◽  
Shamim Ara ◽  
M.S. Osman ◽  
M. Ali Akbar ◽  
Khaled A. Gepreel
Keyword(s):  
Nonlinear Equations ◽  
Gas Dynamics ◽  
Soliton Solutions

BILINEAR FORM AND SOLITON SOLUTIONS FOR THE COUPLED NONLINEAR KLEIN–GORDON EQUATIONS

2012 ◽  
Vol 26 (15) ◽  
pp. 1250057
Author(s):  
HE LI ◽  
XIANG-HUA MENG ◽  
BO TIAN
Keyword(s):  
Field Theory ◽  
Bilinear Form ◽  
Gordon Equation ◽  
Relativistic Quantum ◽  
Soliton Solutions ◽  
Relativistic Quantum Mechanics ◽  
Klein Gordon ◽  
Truncated Painlevé Expansion ◽  
Klein Gordon Equation ◽  
Singular Manifolds

With the coupling of a scalar field, a generalization of the nonlinear Klein–Gordon equation which arises in the relativistic quantum mechanics and field theory, i.e., the coupled nonlinear Klein–Gordon equations, is investigated via the Hirota method. With the truncated Painlevé expansion at the constant level term with two singular manifolds, the coupled nonlinear Klein–Gordon equations are transformed to a bilinear form. Starting from the bilinear form, with symbolic computation, we obtain the N-soliton solutions for the coupled nonlinear Klein–Gordon equations.

scholarly journals Compactons and topological solitons of the Drinfel'd–Sokolov system

2014 ◽  
Vol 19 (2) ◽  
pp. 209-224
Author(s):  
Mustafa Inc ◽  
Eda Fendoglu ◽  
Houria Triki ◽  
Anjan Biswas
Keyword(s):  
Elliptic Function ◽  
Function Method ◽  
Soliton Solutions ◽  
Ansatz Method ◽  
Topological Soliton ◽  
Topological Solitons ◽  
Wave Solutions

This paper presents the Drinfel’d–Sokolov system (shortly D(m, n)) in a detailed fashion. The Jacobi’s elliptic function method is employed to extract the cnoidal and snoidal wave solutions. The compacton and solitary pattern solutions are also retrieved. The ansatz method is applied to extract the topological 1-soliton solutions of the D(m, n) with generalized evolution. There are a couple of constraint conditions that will fall out in order to exist the topological soliton solutions.

A METHOD TO CONSTRUCT WEIERSTRASS ELLIPTIC FUNCTION SOLUTION FOR NONLINEAR EQUATIONS

2011 ◽  
Vol 25 (14) ◽  
pp. 1931-1939 ◽  
Author(s):  
LIANG-MA SHI ◽  
LING-FENG ZHANG ◽  
HAO MENG ◽  
HONG-WEI ZHAO ◽  
SHI-PING ZHOU
Keyword(s):  
Nonlinear Equations ◽  
Elliptic Function ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Order Derivative ◽  
First Order ◽  
Function Solution ◽  
Weierstrass Elliptic Function ◽  
Klein Gordon

A method for constructing the solutions of nonlinear evolution equations by using the Weierstrass elliptic function and its first-order derivative was presented. This technique was then applied to Burgers and Klein–Gordon equations which showed its efficiency and validality for exactly some solving nonlinear evolution equations.

scholarly journals The soliton solution of a modified nonlinear schrödinger equation

2017 ◽  
Vol 5 (1) ◽  
pp. 16
Author(s):  
Jumei Zhang ◽  
Li Yin
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Equations ◽  
Nonlinear Schrödinger Equation ◽  
Soliton Solution ◽  
Schrodinger Equation ◽  
Soliton Solutions ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Derivative Method ◽  
Hirota Bilinear

Hirota bilinear derivative method can be used to construct the soliton solutions for nonlinear equations. In this paper we construct the soliton solutions of a modified nonlinear Schrödinger equation by bilinear derivative method.

Dispersive traveling wave solutions of nonlinear optical wave dynamical models

2019 ◽  
Vol 33 (10) ◽  
pp. 1950120 ◽  
Author(s):  
Wilson Osafo Apeanti ◽  
Dianchen Lu ◽  
David Yaro ◽  
Saviour Worianyo Akuamoah
Keyword(s):  
Physical Properties ◽  
Nonlinear Equations ◽  
Traveling Wave ◽  
Nonlinear Optical ◽  
Soliton Solutions ◽  
Traveling Wave Solutions ◽  
Mathematical Physics ◽  
Dynamical Models ◽  
Optical Wave ◽  
Wave Solutions

In this work, we apply the extended simple equation method to study the dispersive traveling wave solutions of (2+1)-dimensional Nizhnik–Novikov–Vesselov (NNV), Caudrey–Dodd–Gibbon (CDG) and Jaulent–Miodek (JM) hierarchy nonlinear equations. A set of exact, periodic and soliton solutions is obtained for these models confirming the effectiveness of the proposed method. The models studied are important for a number of application areas especially in the field of mathematical physics. Interesting figures are used to illustrate the physical properties of some obtained results. A comparison between obtained solutions and established results in the literature is also given.

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