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

• Published in: International 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
• Language: English
• 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
• ISSN: 0217-9792; 1793-6578
• DOI: 10.1142/S021797922150079X

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.