Applications of some transformations for several variable-coefficient nonlinear evolution equations from plasma physics, arterial mechanics, nonlinear optics and Bose–Einstein condensates

In order to construct exact soliton solutions of nonlinear evolution equations with variable coefficients. By using a transformation, the variable coefficient KdV equation with forced Term is reduced to nonlinear ordinary differential equation (NLODE), after that, a number of exact solitons solutions of variable coefficient KdV equation with forced Term are obtained by using the equation shorted in NLODE. As it showed above, this kind of method can be applied in solving a large number of nonlinear evolution equations.

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Dispersive dark optical soliton with Tzitzéica type nonlinear evolution equations arising in nonlinear optics

Optical and Quantum Electronics ◽

10.1007/s11082-016-0371-y ◽

2016 ◽

Vol 48 (2) ◽

Cited By ~ 38

Author(s):

Jalil Manafian ◽

Mehrdad Lakestani

Keyword(s):

Nonlinear Optics ◽

Evolution Equations ◽

Nonlinear Evolution ◽

Optical Soliton ◽

Nonlinear Evolution Equations

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Solitary wave solutions in plasma physics and acoustic gravity waves of some nonlinear evolution equations through enhanced MSE method

Journal of Physics Communications ◽

10.1088/2399-6528/ab5eac ◽

2019 ◽

Vol 3 (12) ◽

pp. 125011

Author(s):

Md Shafiqul Islam ◽

Md Mamunur Roshid ◽

A K M Lutfor Rahman ◽

M Ali Akbar

Keyword(s):

Solitary Wave ◽

Plasma Physics ◽

Gravity Waves ◽

Evolution Equations ◽

Nonlinear Evolution ◽

Nonlinear Evolution Equations ◽

Solitary Wave Solutions ◽

Acoustic Gravity Waves ◽

Wave Solutions

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A Direct Transformation Method and its Application to Variable Coefficient Nonlinear Equations of Schrödinger Type

Zeitschrift für Naturforschung A ◽

10.1515/zna-2009-1105 ◽

2009 ◽

Vol 64 (11) ◽

pp. 697-708 ◽

Cited By ~ 1

Author(s):

Li-Hua Zhang ◽

Xi-Qiang Liu

Keyword(s):

Differential Equations ◽

Ordinary Differential Equations ◽

Variable Coefficient ◽

Evolution Equations ◽

Nonlinear Evolution ◽

Transformation Method ◽

Nonlinear Evolution Equations ◽

Nls Equation ◽

Direct Transformation ◽

Nonlinear Schrödinger

In this paper, the generalized variable coefficient nonlinear Schrödinger (NLS) equation and the cubic-quintic nonlinear Schrödinger (CQNLS) equation with variable coefficients are directly reduced to simple and solvable ordinary differential equations by means of a direct transformation method. Taking advantage of the known solutions of the obtained ordinary differential equations, families of exact nontravelling wave solutions for the two equations have been constructed. The characteristic feature of the direct transformation method is, that without much extra effort, we circumvent the integration by directly reducing the variable coefficient nonlinear evolution equations to the known ordinary differential equations. Another advantage of the method is that it is independent of the integrability of the given nonlinear equation. The method used here can be applied to reduce other variable coefficient nonlinear evolution equations to ordinary differential equations.

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ON A VARIABLE-COEFFICIENT MODIFIED KP EQUATION AND A GENERALIZED VARIABLE-COEFFICIENT KP EQUATION WITH COMPUTERIZED SYMBOLIC COMPUTATION

International Journal of Modern Physics C ◽

10.1142/s0129183101002024 ◽

2001 ◽

Vol 12 (06) ◽

pp. 819-833 ◽

Cited By ~ 6

Author(s):

YI-TIAN GAO ◽

BO TIAN

Keyword(s):

Symbolic Computation ◽

Variable Coefficient ◽

Evolution Equations ◽

Nonlinear Evolution ◽

Analytic Solutions ◽

Nonlinear Evolution Equations ◽

Hyperbolic Function ◽

Kp Equation ◽

Exact Analytic Solutions ◽

Hyperbolic Function Method

The variable-coefficient nonlinear evolution equations, although realistically modeling various mechanical and physical situations, often cause some well-known powerful methods not to work efficiently. In this paper, we extend the power of the generalized hyperbolic-function method, which is based on the computerized symbolic computation, to a variable-coefficient modified Kadomtsev–Petviashvili (KP) equation and a generalized variable-coefficient KP equation. New exact analytic solutions thus come out.

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MODIFIED EXP-FUNCTION METHOD AND VARIABLE-COEFFICIENT KORTEWEG–DE VRIES MODEL FROM BOSE–EINSTEIN CONDENSATES

International Journal of Modern Physics B ◽

10.1142/s0217979210056281 ◽

2010 ◽

Vol 24 (19) ◽

pp. 3759-3768 ◽

Cited By ~ 2

Author(s):

KE-JIE CAI ◽

CHENG ZHANG ◽

TAO XU ◽

HUAN ZHANG ◽

BO TIAN

Keyword(s):

Variable Coefficient ◽

Function Method ◽

Evolution Equations ◽

Periodic Wave ◽

Nonlinear Evolution Equations ◽

Periodic Wave Solutions ◽

Nonlinear Excitations ◽

De Vries ◽

Bose Einstein ◽

Graphical Illustration

The amplitude of nonlinear excitations in BECs with inhomogeneities is governed by a generalized variable-coefficient Korteweg–de Vries model. With symbolic computation, the Exp-function method is modified to obtain analytical nontraveling solitary-wave and periodic-wave solutions. Through the qualitative analysis and graphical illustration, the inhomogeneous propagation features of solitary waves are discussed, and some observable effects for BEC dynamic in the presence of external potentials are provided. The modified Exp-function method is also applicable to other variable-coefficient nonlinear evolution equations.

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New Soliton-like Solutions of Variable Coefficient Nonlinear Schrödinger Equations

Zeitschrift für Naturforschung A ◽

10.1515/zna-2004-4-502 ◽

2004 ◽

Vol 59 (4-5) ◽

pp. 196-202 ◽

Cited By ~ 4

Author(s):

Heng-Nong Xuan ◽

Changji Wang ◽

Dafang Zhang

Keyword(s):

Exact Solutions ◽

Symbolic Computation ◽

Variable Coefficient ◽

Schrodinger Equation ◽

Evolution Equations ◽

Nonlinear Evolution ◽

Nonlinear Evolution Equations ◽

Nonlinear Schrödinger ◽

System Method ◽

Nonlinear Schrodinger Equations

The improved projective Riccati system method for solving nonlinear evolution equations (NEEs) is established. With the help of symbolic computation, one can obtain more exact solutions of some NEEs. To illustrate the method, we take the variable coefficient nonlinear Schrödinger equation as an example, and obtain four families of soliton-like solutions. Eight figures are given to illustrate some features of these solutions.

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