Abstract:
We present an integrable discretization of a multicomponent discrete complex short-pulse (dCSP) equation in terms of a Lax pair representation and a Darboux transformation (DT). The Lax pair representation is explored using block matrices by extending the $2\times2$ Lax matrices to $2^L\times2^L$ Lax matrices. The DT on the matrix solutions is studied and is used to generate solutions of the multicomponent dCSP equation by using the properties of quasideterminants. By expanding the quasideterminants, we then show the soliton solutions to be expressed as ratios of ordinary determinants. Further, an appropriate continuum limit is applied to obtain multisoliton solutions of the continuous complex short-pulse equation.
Keywords:discrete integrable systems, Darboux transformation, discrete complex short-pulse equation, loop solutions, bright and dark soliton solutions, cuspon solutions.
Fulltext:
PDF file (3138 kB)
First page:
PDF file