A Post-Newtonian Expansion Including Radiation Damping for a Collisionless Plasma

Bauer, Sebastian

doi:10.1007/s00332-019-09580-1

Cited by 3 publications

(1 citation statement)

References 56 publications

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“…Nonlinear phenomena exist widely in nature, and nonlinear partial differential equations (NLPDEs) are indispensable tools to describe the nonlinear phenomena. Nowadays, NLPDEs are widely used in water waves [1], elastic mechanics [2], quantum mechanics [3], plasma physics [4,5], nonlinear optics [6,7], communication engineering [8,9], biomedicine [10] and other fields [11][12][13]. It is well known that in some real-world problems, NLPDEs with variable coefficients provide a more realistic perspective on the inhomogeneities of media and non-uniformities of boundaries in comparison than NLPDEs with constant coefficients, and have applications in various fields such as optical fibers [14], propagations of wave and rogue waves [15], and various other physical systems [16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Various nonlinear characteristics of breather/rogue waves and controllable interaction phenomena for a new KdV equation with variable coeffcients

Lv,

Yue,

Zhang

et al. 2024

Phys. Scr.

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In this paper, we investigate and analyze various nonlinear phenomena of a new (2+1)-dimensional KdV equation with variable coefficients, and successfully obtain breather/rogue wave solutions and interaction solutions of the KdV equation by using the bilinear neural network method and symmetry transformation. Subsequently, we analyze the dynamical characteristics and evolution process of these obtained solutions through the 3-D animations, and find a series of interesting nonlinear phenomena concerning breather/rogue waves, such as fission, regeneration, annihilation, collision, and controllable interaction phenomena on nonzero backgrounds. This paper provides a more intuitive understanding for the nonlinear phenomena of these obtained solutions, and these nonlinear phenomena have potential application value in fluid dynamics, elastic mechanics and other fields of nonlinear science.

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