Group analysis of KdV equation with time dependent coefficients

Johnpillai, A. G.; Khalique, Chaudry Masood

doi:10.1016/j.amc.2010.05.043

Cited by 25 publications

(22 citation statements)

References 13 publications

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“…x )u 0 . Hence (15) does not possess any traveling wave solutions although the equation does manifest the wave breaking phenomenon like its conservative counterpart. It was also shown there that the onset of blow-up is affected by the dissipative parameter γ but the blow-up rate is not affected by γ.…”

Section: Damped-driven Camassa-holm Equationmentioning

confidence: 99%

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Exponential integrators preserving local conservation laws of PDEs with time-dependent damping/driving forces

Bhatt

Moore

2019

Journal of Computational and Applied Mathematics

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Structure-preserving algorithms for solving conservative PDEs with added linear dissipation are generalized to systems with time dependent damping/driving terms. This study is motivated by several PDE models of physical phenomena, such as Korteweg-de Vries, Klein-Gordon, Schrödinger, and Camassa-Holm equations, all with damping/driving terms and time-dependent coefficients. Since key features of the PDEs under consideration are described by local conservation laws, which are independent of the boundary conditions, the proposed (second-order in time) discretizations are developed with the intent of preserving those local conservation laws. The methods are respectively applied to a damped-driven nonlinear Schrödinger equation and a damped Camassa-Holm equation. Numerical experiments illustrate the structure-preserving properties of the methods, as well as favorable results over other competitive schemes.

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Section: Damped-driven Camassa-holm Equationmentioning

confidence: 99%

“…for k ∈ Z + , is used in studies of various physical phenomena, including coastal waves and dipole blocking (see for example [4,15,43]). The equation can be stated in the form (3) with…”

Section: Generalized Kdv Equationsmentioning

confidence: 99%

Exponential integrators preserving local conservation laws of PDEs with time-dependent damping/driving forces

Bhatt

Moore

2019

Journal of Computational and Applied Mathematics

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“…(1.1) using the two approaches as outlined in Section 3. The special cases which are considered here are the results of the group classification of (1.1) performed in [19]. Case 1.…”

Section: Construction Of Conservation Laws For (11)mentioning

confidence: 99%

“…These include the study of the real phenomena such as the coastal waves in ocean, liquid drops and bubbles and in the context of atmospheric blocking phenomenon particularly in the aspect of dipole blocking (see e.g., [17,18]). Lie group classification with respect to the time dependent coefficients of (1.1) was performed in [19]. Our aim in the present work is to construct conservation laws for some special forms of the Eq.…”

Section: Introductionmentioning

confidence: 99%

Conservation laws of KdV equation with time dependent coefficients

Johnpillai

Khalique

2011

Communications in Nonlinear Science and Numerical Simulation

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“…However, literature on nonlinear evolution equations with variable-coefficients [24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39] is rather limited compared to the constant coefficient counterparts. The AKNS hierarchy of nonlinear evolution equations with variable-coefficients has not been much studied.…”

Section: Introductionmentioning

confidence: 99%