Complex Short Pulse Equation and Its Integrable Discretizations
Master's thesis in Applied Mathematics exploring the complex short pulse equation, Lax pair formulation, and N-soliton solutions using Hirota's bilinear method.
Demonstration Videos
bound state
elastic collision
Overview
This thesis investigates the complex short pulse (CSP) equation, presenting its Lax pair and confirming integrability through compatibility conditions. A comprehensive bilinear formulation is developed using Hirota's method, yielding general N-soliton solutions in determinant form. The research demonstrates bound state formation when two solitons have equal velocities and extends the analysis to semi-discrete and fully discrete analogues through discrete hodograph transformations. The work includes visualization of elastic collisions and bound states, contributing to the understanding of integrable systems in mathematical physics.
My Role
Graduate Researcher & Author
Key Highlights
- ✓Confirmed integrability of CSP equation via Lax pair formulation
- ✓Developed bilinear equations using Hirota's method
- ✓Derived general N-soliton solutions in determinant form
- ✓Analyzed bound state formation in two-soliton solutions
- ✓Constructed semi-discrete and fully discrete analogues
- ✓Created visualizations of elastic collisions and bound states
- ✓Published thesis with 102+ downloads on ScholarWorks @ UTRGV