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Oscillation Criteria For First-Order Forced Nonlinear Difference Equations, Ravi P. Agarwal, Said R. Grace, Tim Smith
Oscillation Criteria For First-Order Forced Nonlinear Difference Equations, Ravi P. Agarwal, Said R. Grace, Tim Smith
Publications
Some new criteria for the oscillation of first-order forced nonlinear difference equations are established.
Traveling Wavetrains In The Complex Cubic-Quintic Ginzburg-Laundau Equation, S.C. Mancas, S. Roy Choudhury
Traveling Wavetrains In The Complex Cubic-Quintic Ginzburg-Laundau Equation, S.C. Mancas, S. Roy Choudhury
Publications
In this paper we use a traveling wave reduction or a so–called spatial approximation to comprehensively investigate the periodic solutions of the complex cubic–quintic Ginzburg–Landau equation. The primary tools used here are Hopf bifurcation theory and perturbation theory. Explicit results are obtained for the post–bifurcation periodic orbits and their stability. Generalized and degenerate Hopf bifurcations are also briefly considered to track the emergence of global structure such as homoclinic orbits.
Bifurcations And Competing Coherent Structures In The Cubic-Quintic Ginzburg-Landau Equation I: Plane Wave (Cw) Solutions, S.C. Mancas, S. Roy Choudhury
Bifurcations And Competing Coherent Structures In The Cubic-Quintic Ginzburg-Landau Equation I: Plane Wave (Cw) Solutions, S.C. Mancas, S. Roy Choudhury
Publications
Singularity Theory is used to comprehensively investigate the bifurcations of the steady-states of the traveling wave ODEs of the cubic-quintic Ginzburg-Landau equa- tion (CGLE). These correspond to plane waves of the PDE. In addition to the most general situation, we also derive the degeneracy conditions on the eight coefficients of the CGLE under which the equation for the steady states assumes each of the possible quartic (the quartic fold and an unnamed form), cubic (the pitchfork and the winged cusp), and quadratic (four possible cases) normal forms for singularities of codimension up to three. Since the actual governing equations are …
Numerical Simulation Of Nonlinear Elastic Wave Propagation In Piecewise Homogeneous Media, Arkadi Berezovski, Mihhail Berezovski, Juri Engelbrecht
Numerical Simulation Of Nonlinear Elastic Wave Propagation In Piecewise Homogeneous Media, Arkadi Berezovski, Mihhail Berezovski, Juri Engelbrecht
Publications
Systematic experimental work [S. Zhuang, G. Ravichandran, D. Grady, J. Mech. Phys. Solids 51 (2003) 245–265] on laminated composites subjected to high velocity impact loading exhibits the dispersed wave field and the oscillatory behavior of waves with respect to a mean value. Such a behavior is absent in homogeneous solids. An approximate solution to the plate impact in layered heterogeneous solids has been developed in [X. Chen, N. Chandra, A.M. Rajendran, Int. J. Solids Struct. 41 (2004) 4635–4659]. The influence of the particle velocity on many process characteristics was demonstrated. Based on earlier results [A. Berezovski, J. Engelbrecht, G.A. Maugin, …
On Doubly Periodic Solutions Of Quasilinear Hyperbolic Equations Of The Fourth Order, T. Kiguradze, T. Smith
On Doubly Periodic Solutions Of Quasilinear Hyperbolic Equations Of The Fourth Order, T. Kiguradze, T. Smith
Publications
The problem on doubly periodic solutions is considered for a class of quasilinear hyperbolic equations. Effective sufficient conditions of solvability and unique solvability of this problem are established.