Exact Nonlinear Spectral Analysis of Nonsmooth WENO-JS Solutions

Exact solutions of nonlinear interval Volterra integral equations

Exact solutions of (3 +1)-dimensional nonlinear evolution equations

In this paper, the kudryashov method has been used for finding the general exact solutions of nonlinear evolution equations that namely the (3 + 1)-dimensional Jimbo-Miwa equation and the (3 + 1)-dimensional potential YTSF equation, when the simplest equation is the equation of Riccati.

Nonsmooth Analysis of Spectral Functions

Any spectral function can be written as a composition function of a symmetric function f : IR 7→ IR and the eigenvalue function λ(·) : S 7→ IR, often denoted by (f ◦ λ). S is the subspace of n × n symmetric matrices. In this paper, we present some nonsmooth analysis to such spectral functions. Our main results are: (a) (f ◦ λ) is directionally differentiable if f is semidifferentiable; (b) (f ◦...

Exact solutions of nonlinear partial differential equations by singularity analysis

Whether integrable, partially integrable or nonintegrable, nonlinear partial differential equations (PDEs) can be handled from scratch with essentially the same toolbox, when one looks for analytic solutions in closed form. The basic tool is the appropriate use of the singularities of the solutions, and this can be done without knowing these solutions in advance. Since the elaboration of the si...

exact solutions of nonlinear interval volterra integral equations