High-Level Spectral Method for the Fully Nonlinear Waves

Kim, Jang; Park, Sewan; Shen, Zhirong; Kyoung, Johyun; Baquet, Aldric; Lee, Hyungtae; Ha, Yoon-Jin; Park, Jiyong; Kim, Kyong‐Hwan

doi:10.1007/s11804-023-00323-z

Cited by 1 publication

(1 citation statement)

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“…Nonlinear evolution equations can be used to describe nonlinear phenomena and play a vital role in many fields [1][2][3][4]. Nonlinear science involves the related fields of natural sciences and social sciences, mainly including mathematics, medical chemistry, biology, astronomy, physics, economics and other important subject areas, which is to construct the connection between mathematics and other disciplines.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Superposition and Composite Solution Formula for the Generalized (2+1)-Dimensional Variable-Coefficient Fifth-Order KdV Equation

Zhang,

Bao

2024

Preprint

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In this article, we employ the Bell polynomial method to construct its bilinear form, bilinear Bäcklund transformation, Lax pair, the integrability, infinite conservation laws and superposition formula of the generalized (2 + 1)-dimensional variable-coefficient fifth-order KdV equation, which can help us get more properties, increase the diversity of solutions and get more new phenomenon. It applies the Lax pairs to test the complete integrability of the generalized (2 + 1) -dimensional variable-coefficient fifth-order KdV equation. According to the obtained bilinear Bäcklund transformation, infinite conservation laws and nonlinear superposition formula are derived. By using the nonlinear superposition formula of the solution, the double soliton solution is obtained from the single soliton solution of the equation. Utilizing a symbolic computation approach, we get the Lump solution and exponential of compound solution, breather-type solution and rouge wave solution with appropriate values of constant coefficients. The generalized (2 + 1)-dimensional variable - coefficient fifth-order KdV equation analyses the evolution of long waves with modest amplitudes propagating in plasma physics and the motion of waves in fluids and other mediums. Moreover, dusty plasma, oceanography, water engineering, and other nonlinear sciences.

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Section: Introductionmentioning

confidence: 99%