E. V. Krishnan

Analytical and numerical solutions to the Davey–Stewartson equation with power-law nonlinearity

This paper studies the Davey–Stewartson equation. The traveling wave solution of this equation is obtained for the case of power-law nonlinearity. Subsequently, this equation is solved by the exponential function method. The mapping method is then used to retrieve more solutions to the equation. Finally, the equation is studied with the aid of the variational iteration method. The numerical simulations are also given to complete the analysis.

Remarks on a system of coupled nonlinear wave equations

It is shown that a generalized system of coupled KdV‐MKdV equation exhibits solitary wave solutions. It has been shown that an increase in nonlinearity in one variable in a particular fashion does not affect the existence of solitary wave solutions. The periodic traveling wave solutions of the system have also been investigated.

On some diffusion equations

Travelling wave solutions for two nonlinear diffusion equations have been found by a direct method. A new equilibrium solution has been found for the diffusion equation u t =( u 2 ) x x + u ( u -1)(α- u ) and also a singular solution when α=0 in the equilibrium state using the properties of elliptic functions.

On infrasound radiation of shallow water waves

Sound waves generated by low-frequency gravity modes have been studied. It has been shown that the response function is inversely proportional to the fourth power of the wave number.

Group-invariant solutions of a nerve conduction equation

SummaryGroup-invariant solutions of a non-linear nerve conduction equation have been obtained. The results complement the analysis of Villman and Schierwagen (Appl. Math. Lett.,4 (1991) 33).

On Classical Boussinesq Equation

The Classical Boussinesq equation has been taken into consideration for calculating the periodic wave solutions in terms of Jacobian cosine elliptic functions. A relation between the translation speed of the periodic wave and the maximum height of pulse is established. The linear and the solitary wave limits have also been discussed.

Lie Group of Transformations for a KdV–Boussinesq Equation

We consider a combined Korteweg–deVries and Boussinesq equation governing long surface waves in shallow water. Considering traveling wave solutions, the basic equations will be reduced to a second order ordinary differential equation. Using the Lie group of transformations we reduce it to a first order ordinary differential equation and employ a direct method to derive its periodic solutions in terms of Jacobian elliptic functions and their corresponding solitary wave and explode decay mode solutions.

Progressive oscillations on sloping beaches

The propagation of progressive oscillations over sloping beaches with uniform depth has been investigated. Limitations of the linear form has been analysed.

Travelling wave solutions of density dependent diffusion equations

Travelling wave solutions for two nonlinear diffusion equations have been found by a direct method. The behaviour of solutions for these equations withc and the parameter α in the problem varying have been investigated numerically as a boundary value problem. The equilibrium solutions (c=0) of these equations have been found in terms of Weierstrass elliptic functions.

On shallow water waves

Periodic solutions in terms of Jacobian elliptic functions of a combined KdV-Boussinesq equation have been considered and relations between some physical quantities discussed.