Dynamical solitons for the perturbated Biswas–Milovic equation with Kudryashov's law of refractive index using the first integral method

This paper is concerned with the variable coefficients mKdV (VC-mKdV) equation. First, through some transformation we convert VC-mKdV equation into the constant coefficient mKdV equation. Then, using the first integral method we obtain the exact solutions of VC-mKdV equation, such as rational function solutions, periodic wave solutions of triangle function, bell-shape solitary wave solution, kink-shape solitary wave solution, Jacobi elliptic function solutions, and Weierstrass elliptic function solution. Furthermore, with the aid of Mathematica, the extended hyperbolic functions method is used to establish abundant exact explicit solution of VC-mKdV equation. By the results of the equation, the first integral method and the extended hyperbolic function method are extended from the constant coefficient nonlinear evolution equations to the variable coefficients nonlinear partial differential equation.

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The first integral method and traveling wave solutions to Davey–Stewartson equation

Nonlinear Analysis Modelling and Control ◽

10.15388/na.17.2.14067 ◽

2012 ◽

Vol 17 (2) ◽

pp. 182-193 ◽

Cited By ~ 31

Author(s):

Hossein Jafari ◽

Atefe Sooraki ◽

Yahya Talebi ◽

Anjan Biswas

Keyword(s):

Exact Solutions ◽

Soliton Solution ◽

Commutative Algebra ◽

Traveling Wave ◽

Integral Method ◽

Traveling Wave Solutions ◽

First Integral ◽

First Integral Method ◽

Wave Solutions

In this paper, the first integral method will be applied to integrate the Davey–Stewartson’s equation. Using this method, a few exact solutions will be obtained using ideas from the theory of commutative algebra. Finally, soliton solution will also be obtained using the traveling wave hypothesis.

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First integral method for non-linear differential equations with conformable derivative

Mathematical Modelling of Natural Phenomena ◽

10.1051/mmnp/2018012 ◽

2018 ◽

Vol 13 (1) ◽

pp. 14 ◽

Cited By ~ 13

Author(s):

H. Yépez-Martínez ◽

J.F. Gómez-Aguilar ◽

Abdon Atangana

Keyword(s):

Differential Equations ◽

Exact Solutions ◽

Integral Method ◽

General Scheme ◽

First Integral ◽

Fractional Partial Differential Equations ◽

Conformable Derivative ◽

First Integral Method ◽

Analytic Treatment ◽

Linear Differential

In this paper, we present an analysis based on the first integral method in order to construct exact solutions of the nonlinear fractional partial differential equations (FPDE) described by beta-derivative. A general scheme to find the approximated solutions of the nonlinear FPDE is showed. The results obtained showed that the first integral method is an efficient technique for analytic treatment of nonlinear beta-derivative FPDE.

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Optical solitons for coupled Fokas–Lenells equation in birefringence fibers

Modern Physics Letters B ◽

10.1142/s0217984919503172 ◽

2019 ◽

Vol 33 (26) ◽

pp. 1950317 ◽

Cited By ~ 3

Author(s):

Nauman Raza ◽

Saima Arshed ◽

Sultan Sial

Keyword(s):

Integral Method ◽

Expansion Method ◽

First Integral ◽

Optical Solitons ◽

Optical Soliton ◽

First Integral Method ◽

Complexiton Solutions ◽

Existence Criterion

This paper discusses bright, dark and singular optical soliton as well as complexiton solutions to the coupled Fokas–Lenells equation (FLE) for birefringent fibers by three integration tools such as [Formula: see text]-expansion method, the first integral method and the sine-Gordon expansion method. The existence criterion of these solutions is also given.

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