AN ALTERNATIVE EXPLICIT CONSTRUCTION OF N-SOLITON SOLUTIONS IN 1+1 DIMENSIONS

Abstract

Using the special Riemann-problem technique of Zakharov et al. [Sov. Phys. JETP 47, 1017 (1978)], an explicit N-step Backlund transformation is derived for a class of 1 + 1-dimensional nonlinear evolution equations, thus providing an alternative explicit expression of their N-soliton solutions which no longer involves computations of the intermediate solutions, nor leaves any expansion of N x N determinants (and their differentiation) to be done.