Exact Solutions Superimposed with Nonlinear Plane Waves

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.

Exact Solutions of Noncommutative Vacuum Einstein Field Equations and Plane-fronted Gravitational Waves

We construct a class of exact solutions of the noncommutative vacuum Einstein field equations, which are noncommutative analogues of the plane-fronted gravitational waves in classical gravity.

Exact solutions for impulsive gravitational waves∗

All impulsive waves (with no tails) in vacuum backgrounds of constant curvature (i.e. Minkowski, de Sitter and anti-de Sitter) are classified according to whether they are expanding or non-expanding. It is demonstrated that the expanding waves may, in some sense, be regarded as impulsive limits of Robinson–Trautman type N solutions.

Degenerate weakly nonlinear elastic plane waves

Weakly nonlinear plane waves are considered in hyperelastic crystals. Evolution equations are derived at a quadratically nonlinear level for the amplitudes of quasi-longitudinal and quasi-transverse waves propagating in arbitrary anisotropic media. The form of the equations obtained depends upon the direction of propagation relative to the crystal axes. A single equation is found for all propag...