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Semianalytical solutions of (2+1)-dimensional KdV–Burgers and Vakhnenko equations

Prince Sharma, Rajan Arora and Amit Tomar
Vol. 14 (2026), No. 3, 427–440
DOI: 10.2140/memocs.2026.14.427
Abstract

We use the homotopy analysis method (HAM) to find analytical solutions to the Vakhnenko equation and the Korteweg–de Vries–Burgers (KdV–Burgers) equation, two well-known (2+1)-dimensional nonlinear evolution equations. These solutions are essential for describing complex physical processes in a variety of fields, including nonlinear optics, fluid dynamics, and plasma physics. The convergence of the HAM-based solution is demonstrated using the squared residual error technique. The HAM-based technique shows a strong match with the exact solution to the problems.

Keywords
Vakhnenko equation, Korteweg–de Vries–Burgers equation, homotopy analysis method, nonlinear PDEs, semianalytical solutions
Mathematical Subject Classification
Primary: 35C10
Secondary: 35L05
Milestones
Received: 30 September 2025
Revised: 13 January 2026
Accepted: 11 April 2026
Published: 16 June 2026

Communicated by Mario Spagnuolo
Authors
Prince Sharma
Department of Applied Mathematics and Scientific Computing
Indian Institute of Technology Roorkee
Roorkee
India
Rajan Arora
Department of Applied Mathematics and Scientific Computing
Indian Institute of Technology Roorkee
Roorkee
India
Amit Tomar
Department of Mathematics
School of Computer Science Engineering and Technology
Bennett University
Greater Noida
India
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