Integrability analysis and soliton solutions of the complex short pulse equation and its two-component expansion

When

April 4th, 2025 | 3:00 p.m. – 3:30 p.m.
Refreshments provided

Where

University Hall 4002

Speaker

Arham Amin, UAB graduate student

Abstract

In this talk, we investigate soliton solutions to a two-component complex short pulse (c-SP) equation. Based on the known Lax pair representation of this equation, we verify the integrability of a two-component c-SP equation and find an equivalent convenient Lax pair through hodograph transformation. The Darboux transformation (DT) is utilized to construct multi-soliton solutions for the two-component c-SP equation in terms of ordinary determinants. Furthermore, one-soliton and two-soliton solutions are presented in detail and generalized for N-fold soliton solutions. We also derive exact soliton solutions in explicit form using suitable reduction constraints from various “seed” solutions.

*All UAB students, faculty and guests are invited.