Abstract
Kadomtsev–Petviashvili (KP) equation is an important fluid equation. In the framework of Lax scheme, this paper first derives a new and more general variable-coefficient KP (vcKP) equation. Then the inverse scattering transform (IST) and the F-expansion method are respectively used to construct exact wave solutions of a special case of the derived vcKP equation and its extended case in which the constraint relationships between the coefficient functions are further weakened. The obtained wave solutions include rational solutions, which are constructed not only by the IST but also by the F-expansion method, and Jacobi elliptic function solutions. In the limit cases of the modulus parameter, the obtained Jacobi elliptic function solutions degenerate into hyperbolic function solutions and trigonometric function solutions as well as rational solutions. To gain more insights into some of the obtained solutions, dynamical evolution with novle features like the Z-shaped flat like-lump soliton and the inclined double periodic wave of whose are shown directly by pictures. The significance of this paper is to extend IST to the high-dimensional models with variable coefficients by taking the vcKP equation as an example, and obtain some new solutions and their novel solution structres of the vcKP equation by using the IST and the F-expansion method.
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Acknowledgements
This work was supported by the Liaoning BaiQianWan Talents Program of China (2019Year), the National Science Foundation of China (11547005), the Natural Science Foundation of Education Department of Liaoning Province of China (LJ2020002) and the Natural Science Foundation of Xinjiang Autonomous Region of China (2020D01B01).
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Zhang, S., Zhang, D. Analytical methods for the variable-coefficient KP equation and its wave solutions in weakly dispersive media. Int J Geomath 12, 13 (2021). https://doi.org/10.1007/s13137-021-00182-2
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DOI: https://doi.org/10.1007/s13137-021-00182-2
Keywords
- vcKP equation
- Rational solution
- Jacobi elliptic function solution
- Hyperbolic function solution
- Trigonometric function solution