Exact Analytic N-Soliton-Like Solution in Wronskian Form for a Generalized Variable-Coefficient Korteweg-de Vries Model from Plasmas and Fluid Dynamics

Applicable in fluid dynamics and plasmas, a generalized variable-coefficient Korteweg-de Vries （vcKdV） model is investigated. The bilinear form and analytic N-soliton-like solution for such a model are derived by the Hirota method and Wronskian technique. Additionally, the bilinear auto-Bǎcklund transformation between （N-1）- soliton-like and N-soliton-like solutions is verified.     

Painleve Property and New Analytic Solutions for a Variable-Coefficient Kadomtsev--Petviashvili Equation with Symbolic Computation

A variable-coemcient Kadomtsev-Petviashvili equation is investigated. The Painlev6 analysis leads to its explicit Painlevd-integrable conditions. An auto-Backlund transformation and the bilinear form are presented via the truncated Painlev6 expansion and symbolic computation. Several families of new analytic solutions arepresented, including the soliton-like and periodic solutions.     

Existence of Formal Conservation Laws of a Variable-Coefficient Korteweg--de Vries Equation from Fluid Dynamics and Plasma Physics via Symbolic Computation

Employing the method which can be used to demonstrate the infinite conservation laws for the standard Kortewegde Vries （KdV） equation, we prove that the variable-coeFficient KdV equation under the Painlevé test condition also possesses the formal conservation laws.