We propose a new approach to models of general compressible viscous fluids based on the concept dissipative solutions. These are weak solutions satisfying underlying equations modulo defect measure. A solution coincides with strong as long latter exists (weak–strong uniqueness) and they solve problem in classical sense soon smooth (compatibility). We consider non–li...

Infinitely many cases for which two independent fundamental solutions of the biconfluent Heun equation can each be presented as an irreducible linear combination confluent generalized hypergeometric functions are identified. The involved functions, in general do not reduce to polynomials, such that numerator parameter (except one) exceeds a corresponding denominator by unity.

An analytic study was conducted on coupled partial differential equations. We formally derived new solitary wave solutions of generalized coupled system of Zakharov-Kuznetsov (ZK) and KdV equations by using modified extended tanh method. The traveling wave solutions for each generalized coupled system of ZK and KdV equations are shown in form of periodic, dark, and bright solitary wave solution...

In this paper, a generalized KdV equation with time-dependent coefficients will be studied. The K(m,n) equation with generalized evolution will also be examined. The Riccati equation mapping method will be used to obtain some new exact solutions for both equations. These solutions include solitary wave solutions and periodic wave solutions. The results presented in this paper improve the previo...

Two classes of rational solutions to a KdV-like nonlinear differential equation are constructed. The basic object is a generalized bilinear differential equation based on a prime number p 1⁄4 3. A conjecture is made that the two presented classes of rational solutions contain all rations solutions to the considered KdV-like equation, which are generated from polynomial solutions to the correspo...

We investigate generalizations of the Burgers and Burgers-Huxley equations. The investigations we offer focus attention mainly on presenting explict analytical solutions by means of relating these generalized equations to relativistic 1 + 1 dimensional systems of scalar fields where topological solutions are known to play a role. Emphasis is given on chiral solutions, that is, on the possibilit...