Under investigation in this paper is a variable-coefficient coupled Gross–Pitaevskii (GP) system, which is associated with the studies on atomic matter waves. Through the Painlevé analysis, we obtain the constraint on the variable coefficients, under which the system is integrable. The bilinear form and multi-soliton solutions are derived with the Hirota bilinear method and symbolic computation...

In this article we give a brief survey of breather and soliton solutions to the Ricci flow and prove a no breather and soliton theorem for homogeneous solutions.

This paper investigates a cylindrical nonlinear Schrödinger (cNLS) equation, which describes the cylindrically diverging quasi-plane envelope waves in a nonlinear medium. With the Hirota method and symbolic computation, bilinear form and N-soliton solutions in the form of an Nth-order polynomial in N exponentials are obtained for the cNLS equation. By means of the properties of double Wronskian...

A different kind of shape changing (intensity redistribution) collision with potential application to signal amplification is identified in the integrable -coupled nonlinear Schrödinger (CNLS) equations with mixed signs of focusing- and defocusing-type nonlinearity coefficients. The corresponding soliton solutions for the N=2 case are obtained by using Hirota's bilinearization method. The disti...