Exact solutions of nonlinear differential equations are of great importance to the theory and
practice of complex systems. The main point of this review article is to discuss a specific …

On the basis of the spectral analysis of the 4 * 4 4× 4 Lax pair associated with the spin-1
Gross–Pitaevskii equation and the scattering matrix, the solution to the Cauchy problem of …

This investigation focuses on two novel Kadomtsev–Petviashvili (KP) equations with time-
dependent variable coefficients that describe the nonlinear wave propagation of small …

This book is the written and somewhat expanded version of the author's lectures delivered at
the NSF-CBMS international research conference organized at the Mathematics Department …

Peakons (peaked solitons) are particular solutions admitted by certain nonlinear PDEs, most
famously the Camassa–Holm shallow water wave equation. These solutions take the form of …

In this paper, we present a systematical inverse scattering transform for both focusing and
defocusing nonlocal (reverse-space–time) modified Korteweg–de Vries (mKdV) equations …

In this paper, we study the soliton resolution and large time behavior of solutions to the
Cauchy problem for the Novikov equation with a nonzero background ut− utx x+ 4 ux= 3 …

It is known that both the Sawada–Kotera equation and the Kaup–Kupershmidt equation are
related with the same modified equation by different Miura transformations. There is …

Based on the non-semisimple Lie algebra g˜, we introduce a new integrable coupling
system of the focusing nonlinear Schrödinger equation associated with a 4th-order block …

We present an inverse scattering transform approach to the Cauchy problem on the line for
the Degasperis--Procesi equation $ u_t-u_ {txx}+ 3\omega u_x+ 4uu_x= 3u_xu_ {xx}+ uu …