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Full-Text Articles in Physical Sciences and Mathematics
Spatiotemporal Structure Of Pulsating Solitons In The Cubic-Quintic Ginzburg-Landau Equation: A Novel Variational Formulation, S.C. Mancas, S. Roy Choudhury
Spatiotemporal Structure Of Pulsating Solitons In The Cubic-Quintic Ginzburg-Landau Equation: A Novel Variational Formulation, S.C. Mancas, S. Roy Choudhury
Publications
Comprehensive numerical simulations (reviewed in Dissipative Solitons, Akhmediev and Ankiewicz (Eds.), Springer, Berlin, 2005) of pulse solutions of the cubic–quintic Ginzburg–Landau Equation (CGLE), a canonical equation governing the weakly nonlinear behavior of dissipative systems in a wide variety of disciplines, reveal various intriguing and entirely novel classes of solutions. In particular, there are five new classes of pulse or solitary waves solutions, viz. pulsating, creeping, snake, erupting, and chaotic solitons. In contrast to the regular solitary waves investigated in numerous integrable and non-integrable systems over the last three decades, these dissipative solitons are not stationary in time. Rather, they are …
Bifurcations Of Plane Wave (Cw) Solutions In The Complex Cubic-Quintic Ginzburg-Landau Equation, S.C. Mancas, S. Roy Choudhury
Bifurcations Of Plane Wave (Cw) Solutions In The Complex Cubic-Quintic Ginzburg-Landau Equation, 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 …
The Complex Cubi-Quintic Ginzburg-Landau Equation: Hopf Bifurcations Yielding Traveling Waves, S.C. Mnacas, S. Roy Choudhury
The Complex Cubi-Quintic Ginzburg-Landau Equation: Hopf Bifurcations Yielding Traveling Waves, S.C. Mnacas, S. Roy Choudhury
Publications
In this paper we use a traveling wave reduction or a so{called spatial approxima- tion 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 brie y considered to track the emergence of global structure such as homoclinic orbits.
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 …