Physical Sciences and Mathematics | Open Access Articles

Pulses And Snakes In Ginzburg-Landau Equation, S.C. Mancas, Roy S. Choudhury Jan 2015

Pulses And Snakes In Ginzburg-Landau Equation, S.C. Mancas, Roy S. Choudhury

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Using a variational formulation for partial differential equations combined with numerical simulations on ordinary differential equations (ODEs), we find two categories (pulses and snakes) of dissipative solitons, and analyze the dependence of both their shape and stability on the physical parameters of the cubic-quintic Ginzburg–Landau equation (CGLE). 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 spatially confined pulse-type structures whose envelopes exhibit complicated temporal dynamics. Numerical simulations reveal very interesting bifurcations sequences as the parameters of the CGLE …

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Nonlinear Equations And Wavelets, Andrei Ludu Jan 2003

Nonlinear Equations And Wavelets, Andrei Ludu

Andrei Ludu

No abstract provided.

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Nonlinear Phenomena In Nuclei: The Antisoliton Model For Fission, Andrei Ludu Jan 1999

Nonlinear Phenomena In Nuclei: The Antisoliton Model For Fission, Andrei Ludu

Andrei Ludu

No abstract provided.

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Patterns On Liquid Surfaces: Cnoidal Waves, Compactons And Scaling, Andrei Ludu Jan 1998

Patterns On Liquid Surfaces: Cnoidal Waves, Compactons And Scaling, Andrei Ludu

Andrei Ludu

Localized patterns and nonlinear oscillation formation on the bounded free surface of an ideal incompressible liquid are analytically investigated. Cnoidal modes, solitons and compactons, as traveling non-axially symmetric shapes are discussed. A finite-difference differential generalized Korteweg-de Vries equation is shown to describe the three-dimensional motion of the fluid surface and the limit of long and shallow channels one re-obtains the well-known KdV equation. A tentative expansion formula for the representation of the general solution of a nonlinear equation, for given initial condition is introduced on a graphical-algebraic basis. The model is useful in multilayer fluid dynamics, cluster formation, and nuclear …

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Alpha+28si Cluster Structure As Solitons On The Nuclear Surface, Andrei Ludu Jan 1995