Interaction solutions to nonlinear partial differential equations via Hirota bilinear forms: one-lump-multi-stripe and one-lump-multi-soliton types

• Published in: Nonlinear dynamics Vol. 103; no. 1; pp. 947 - 977
• Main Authors: Lü, Xing, Chen, Si-Jia
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 2021; Springer Nature B.V
• Subjects: Automotive Engineering; Classical Mechanics; Control; Dynamical Systems; Engineering; Exact solutions; Exponential functions; Mathematical analysis; Mechanical Engineering; Nonlinear differential equations; Nonlinear equations; Original Paper; Partial differential equations; Quadratic equations; Solitary waves; Trigonometric functions; Vibration; Interaction solution; 35A25; Soliton; Integrable equation; Nonlinear partial differential equation; Hirota bilinear form; 35Q51; 37K10
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-020-06068-6

Interaction solutions between lump and soliton are analytical exact solutions to nonlinear partial differential equations. The explicit expressions of the interaction solutions are of value for analysis of the interacting mechanism. We analyze the one-lump-multi-stripe and one-lump-multi-soliton solutions to nonlinear partial differential equations via Hirota bilinear forms. The one-lump-multi-stripe solutions are generated from the combined solution of quadratic functions and N exponential functions, while the one-lump-multi-soliton solutions from the combined solution of quadratic functions and N hyperbolic cosine functions. Within the context of the derivation of the lump solution and soliton solution, necessary and sufficient conditions are presented for the two types of interaction solutions, respectively, based on the combined solutions to the associated bilinear equations. Applications are made for a (2+1)-dimensional generalized KdV equation, the (2+1)-dimensional NNV system and the (2+1)-dimensional Ito equation.