Solitary Waves in Dispersive Complex Media

Belashov, V. Yu.; Vladimirov, Sergey V.

doi:10.1007/b138237

Cited by 114 publications

(93 citation statements)

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“…Hence, certain constraints on the variable-coefficient functions are needed to be constructed in hope that the variable-coefficient NLEEs become still integrable. In the present paper, based on the Bäcklund transformation and the inverse scattering scheme, two constraints on the variable-coefficient functions of (10) [13]). …”

Section: Conclusion and Discussionmentioning

confidence: 99%

Symbolic Computation Study of a Generalized Variable-Coefficient Two-Dimensional Korteweg-de Vries Model with Various External-Force Terms from Shallow Water Waves, Plasma Physics, and Fluid Dynamics

Yao

et al. 2009

Zeitschrift Für Naturforschung A

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The variable-coefficient two-dimensional Korteweg-de Vries (KdV) model is of considerable significance in describing many physical situations such as in canonical and cylindrical cases, and in the propagation of surface waves in large channels of varying width and depth with nonvanishing vorticity. Under investigation hereby is a generalized variable-coefficient two-dimensional KdV model with various external-force terms. With the extended bilinear method, this model is transformed into a variable-coefficient bilinear form, and then a Bäcklund transformation is constructed in bilinear form. Via symbolic computation, the associated inverse scattering scheme is simultaneously derived on the basis of the aforementioned bilinear Bäcklund transformation. Certain constraints on coefficient functions are also analyzed and finally some possible cases of the external-force terms are discussed. Among the most important models of nonlinear evolution equations (NLEEs), constant-coefficient Korteweg-de Vries (KdV) and KdV-type equations are encountered in many apparently unrelated phenomena in different physical areas such as shallow water waves, plasmas, fluids and lattice vibrations of a crystal at low temperatures [1]. In all of these applications, the physical situations described via the KdV (or KdVtype) models tend to be highly idealized, owing to the assumption of constant coefficients. Considering the inhomogeneities of media, nonuniformities of boundaries and external forces, the variable-coefficient models are much more powerful and realistic than their constant-coefficient counterparts in describing various 0932-0784 / 09 / 0300-0222 $ 06.00 c 2009 Verlag der Zeitschrift für Naturforschung, Tübingen · http://znaturforsch.com situations, e. g., in the coastal waters of oceans, space and laboratory plasmas, superconductors and opticalfiber communications [2 -6].In the past decades, it has been shown that various physical phenomena in nature, actual physics and engineering can be described by the variable-coefficient KdV model with perturbed, dissipative and externalforce terms as [7] where v(x,t) is a function of the variables x and t, µ 1 (t) = 0, µ 2 (t) = 0, µ 3 (t), µ 4 (t) and µ 5 (t) represent the coefficients of the nonlinear, dispersive, dissipative, perturbed and external-force terms, respectively, all of which are real functions. In recent studies, of physical and mechanical interests, many important examples of (1), among others, can be listed [8]:Unauthenticated Download Date | 5/8/18 5:12 AM

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Section: Conclusion and Discussionmentioning

confidence: 99%

Symbolic Computation Study of a Generalized Variable-Coefficient Two-Dimensional Korteweg-de Vries Model with Various External-Force Terms from Shallow Water Waves, Plasma Physics, and Fluid Dynamics

Yao

et al. 2009

Zeitschrift Für Naturforschung A

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“…In the absence of collisions, i.e., Γ = 0, one recovers the usual KdV equation for ion-acoustic wave in ultra-relativistic degenerate dense plasma (Nahar et al 2013). A usual KdV equation represents a Hamiltonian system that is completely integrable and obeys infinite conservation laws (Belashov and Vladimirov 2005). Here, we consider the energy conservation law by neglecting the dissipation effects (Γ = 0) in Eq.…”

Section: Nonlinear Modelmentioning

confidence: 97%

Weakly dissipative solitons in dense relativistic-degenerate plasma

Ahmad

Ata-ur-Rahman

Khan

2015

Astrophys Space Sci

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We investigate the features of weakly nonlinear waves in a collisional dense plasma consisting of ultrarelativistic degenerate electrons and non-relativistic degenerate ions. In weak dissipation limit, the dynamics of low frequency nonlinear ion (solitary) wave is described by solving a damped Korteweg-deVries equation. The analytical and numerical analysis shows the existence of weakly dissipative solitons evolving with time. The characteristics of soliton evolution with plasma number density and slow ionneutral collision rate are discussed with some detail. The relevance of the study with degenerate plasmas in ultra-dense astrophysical objects, particularly white dwarf stars is also pointed out.

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“…TID directly affect variability of the ionospheric parameters as well as those of the Earth's ionosphere waveguide. One of the most convenient approaches to these problems is to study TID dynamics in terms of the internal gravity waves (IGW) (Belashov and Vladimirov, 2005). Of special interest are the IGW solitons as traveling in the F-layer stable large-scale wave formations, caused by various reasons such as the isolated magnetic substorms, solar terminator and solar eclipse (Belashova and Belashov, 2006), seismo-volcanic processes, and high-power artificial explosions (Belashov and Vladimirov, 2005;Belashova and Belashov, 2006).…”

Section: Introductionmentioning

confidence: 99%