Integrability aspects and some abundant solutions for a new (4 + 1)-dimensional KdV-like equation

In this paper, we introduce a new (4 + 1)-dimensional KdV-like equation. By using the Bell Polynomial method, we obtain the bilinear form, bilinear Bäcklund transformation, Lax pair and infinite conservation laws. It is proved that the equation is completely integrable in Lax pair sense. Based on th...

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Published inInternational journal of modern physics. B, Condensed matter physics, statistical physics, applied physics Vol. 35; no. 6; p. 2150079
Main Authors Han, Peng-Fei, Bao, Taogetusang
Format Journal Article
LanguageEnglish
Published Singapore World Scientific Publishing Company 10.03.2021
World Scientific Publishing Co. Pte., Ltd
Subjects
Combinatorial analysis
Conservation laws
Dynamic models
Integral calculus
Korteweg-Devries equation
Nonlinear evolution equations
Polynomials
Solitary waves
(4 + 1)-Dimensional KdV-like equation
infinite conservation laws
high-order lump solutions and their interaction solutions
different types of
Bäcklund transformation
soliton solutions
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Abstract In this paper, we introduce a new (4 + 1)-dimensional KdV-like equation. By using the Bell Polynomial method, we obtain the bilinear form, bilinear Bäcklund transformation, Lax pair and infinite conservation laws. It is proved that the equation is completely integrable in Lax pair sense. Based on the Hirota bilinear method and the test function method, high-order lump solutions, high-order lump-kink type N -soliton solutions, high-order lump- cosh - N - cos - M type soliton solutions, exp - cosh - N - cos - M type soliton solutions and exp - tanh - N - sin - M type soliton solutions ( N , M → ∞ ) for this equation are obtained with the help of symbolic computation. Via three-dimensional plots and contour plots with the help of Mathematics, analyses for the obtained solutions are presented, and their dynamic properties are discussed. Many dynamic models can be simulated by nonlinear evolution equations, and these graphical analyses are helpful to understand these models.
AbstractList In this paper, we introduce a new (4 + 1)-dimensional KdV-like equation. By using the Bell Polynomial method, we obtain the bilinear form, bilinear Bäcklund transformation, Lax pair and infinite conservation laws. It is proved that the equation is completely integrable in Lax pair sense. Based on the Hirota bilinear method and the test function method, high-order lump solutions, high-order lump-kink type N -soliton solutions, high-order lump- cosh - N - cos - M type soliton solutions, exp - cosh - N - cos - M type soliton solutions and exp - tanh - N - sin - M type soliton solutions ( N , M → ∞ ) for this equation are obtained with the help of symbolic computation. Via three-dimensional plots and contour plots with the help of Mathematics, analyses for the obtained solutions are presented, and their dynamic properties are discussed. Many dynamic models can be simulated by nonlinear evolution equations, and these graphical analyses are helpful to understand these models.
In this paper, we introduce a new (4 + 1)-dimensional KdV-like equation. By using the Bell Polynomial method, we obtain the bilinear form, bilinear Bäcklund transformation, Lax pair and infinite conservation laws. It is proved that the equation is completely integrable in Lax pair sense. Based on the Hirota bilinear method and the test function method, high-order lump solutions, high-order lump-kink type [Formula: see text]-soliton solutions, high-order lump-[Formula: see text]-[Formula: see text]-[Formula: see text]-[Formula: see text] type soliton solutions, [Formula: see text]-[Formula: see text]-[Formula: see text]-[Formula: see text]-[Formula: see text] type soliton solutions and [Formula: see text]-[Formula: see text]-[Formula: see text]-[Formula: see text]-[Formula: see text] type soliton solutions [Formula: see text] for this equation are obtained with the help of symbolic computation. Via three-dimensional plots and contour plots with the help of Mathematics, analyses for the obtained solutions are presented, and their dynamic properties are discussed. Many dynamic models can be simulated by nonlinear evolution equations, and these graphical analyses are helpful to understand these models.
In this paper, we introduce a new (4 + 1)-dimensional KdV-like equation. By using the Bell Polynomial method, we obtain the bilinear form, bilinear Bäcklund transformation, Lax pair and infinite conservation laws. It is proved that the equation is completely integrable in Lax pair sense. Based on the Hirota bilinear method and the test function method, high-order lump solutions, high-order lump-kink type N-soliton solutions, high-order lump-cosh-N-cos-M type soliton solutions, exp-cosh-N-cos-M type soliton solutions and exp-tanh-N-sin-M type soliton solutions (N,M →∞) for this equation are obtained with the help of symbolic computation. Via three-dimensional plots and contour plots with the help of Mathematics, analyses for the obtained solutions are presented, and their dynamic properties are discussed. Many dynamic models can be simulated by nonlinear evolution equations, and these graphical analyses are helpful to understand these models.
Author Bao, Taogetusang
Han, Peng-Fei
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Keywords (4 + 1)-Dimensional KdV-like equation
infinite conservation laws
high-order lump solutions and their interaction solutions
different types of
Bäcklund transformation
soliton solutions
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Snippet In this paper, we introduce a new (4 + 1)-dimensional KdV-like equation. By using the Bell Polynomial method, we obtain the bilinear form, bilinear Bäcklund...
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SubjectTerms Combinatorial analysis
Conservation laws
Dynamic models
Integral calculus
Korteweg-Devries equation
Nonlinear evolution equations
Polynomials
Solitary waves
Title Integrability aspects and some abundant solutions for a new (4 + 1)-dimensional KdV-like equation
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