In this paper, an analytical technique has been developed based on a modified harmonic balance method to determine higher-order approximate periodic solutions for a nonlinear oscillator with discontinuity for which the elastic force term, is an anti-symmetric and quadratic term. Usually, a set of nonlinear algebraic equations is solved with this method. However, analytical solutions of these al...

The Korteweg-de Vries (KdV) equation is widely recognized as a simple model for unidirectional weakly nonlinear dispersive waves on the surface of a shallow body of fluid. While solutions of the KdV equation describe the shape of the free surface, information about the underlying fluid flow is encoded into the derivation of the equation, and the present article focuses on the formulation of mas...

Anefficient algorithmisdeveloped for solving the systemofdifferential algebraic equations (DAE)describing the dynamics of a reactive distillation (RD) column using the equilibrium tray model. Unlike existing eceived in revised form 23 January 2009 ccepted 27 January 2009 vailable online 4 February 2009 eywords: eactive distillation algorithms, the rate of change of tray specific enthalpy is obt...

S U M M A R Y We investigate the chaotic behaviour of slip pulses that propagate in a spring block slider model with velocity weakening friction by numerically solving a computationally intensive set of n coupled non-linear equations, where n is the number of blocks. We observe that the system evolves into a spatially heterogeneous pre-stress after the occurrence of a sufficient number of event...

In this paper, we originate results with finite difference schemes to approximate the solution of the classical Fisher Kolmogorov Petrovsky Piscounov (KPP) equation from population dynamics. Fisher’s equation describes a balance between linear diffusion and nonlinear reaction. Numerical example illustrates the efficiency of the proposed schemes, also the Neumann stability analysis reveals that ...

We prove the existence of a stationary solution of any given mass to the coagulationfragmentation equation without assuming a detailed balance condition, but assuming instead that aggregation dominates fragmentation for small particles while fragmentation predominates for large particles. We also show the existence of a self similar solution of any given mass to the coagulation equation and to ...

With the help of the generalized hyperbolic function, the subsidiary ordinary differential equation method is improved and proposed to construct exact traveling wave solutions of the nonlinear partial differential equations in a unified way. A class of nonlinear Schrödinger-type equations including the generalized Zakharov system, the Rangwala-Rao equation, and the Chen-Lee-Liu equation are inv...

We give arguments for the existence of exact travelling-wave (in particular solitonic) solutions of a perturbed sine-Gordon equation on the real line or on the circle, and classify them. The perturbation of the equation consists of a constant forcing term and a linear dissipative term. Such solutions are allowed exactly by the energy balance of these terms, and can be observed experimentally e....

We propose two methods to find analytic periodic approximations intended for differential equations of Hill type. Here, we apply these methods on the simplest case of the Mathieu equation. The former has been inspired in the harmonic balance method and designed to find, making use on a given algebraic function, analytic approximations for the critical values and their corresponding periodic sol...

Low–energy cosmic rays (CRs) are confined by self–generated MHD waves in the mostly neutral ISM. We show that the CR transport equation can be expressed as a continuity equation for the CR number density involving an effective convection velocity. Assuming balance between wave growth and ion–neutral damping, this equation gives a steady–state condition ncr ∝ n 1/2 i up to a critical density for...