A variational principle for coupled nonlinear Schrödinger equations with variable coefficients and high nonlinearity

Zhou, Xuliang; Wang, Lin

doi:10.1016/j.camwa.2010.08.062

Cited by 14 publications

(6 citation statements)

References 22 publications

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“…(1.14) with respect to u and w are Similar results can be obtained for the Burgers equation [17] by the semi-inverse method [3]- [6], [8]. Some illustrating examples for construction of Lagrangian of a nonlinear equation are available in Refs [2,7,9,10,11,12,13,14,15,18].…”

Section: Introductionmentioning

confidence: 58%

Lagrangians of the (2+1) -dimensional KP equation with variable coefficients and cross terms

Liu¹,

He²,

Li³

2016

J. Nonlinear Sci. Appl.

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Section: Introductionmentioning

confidence: 58%

Lagrangians of the (2+1) -dimensional KP equation with variable coefficients and cross terms

Liu¹,

He²,

Li³

2016

J. Nonlinear Sci. Appl.

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“…This note shows that the semi-inverse method in [1] works also for the present problem, and it is concluded that the semi-inverse method is a powerful mathematical tool to the construction of a variational formulation for a nonlinear equation; illustrating examples are available in [5][6][7][8][9][10]. The semi-inverse method can be extended to fractional calculus [11][12][13][14].…”

Section: Resultsmentioning

confidence: 95%

A Note on the Semi-Inverse Method and a Variational Principle for the Generalized KdV-mKdV Equation

Yao

Yang

Zhou

2013

Abstract and Applied Analysis

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“…HereT is the kinetic energy operator,V is an external potential, and λ is a coupling constant for inter-particle interactions. Effects of nonlinearity and variational principles for GPE and its generalizations have been widely studied [14][15][16][17][18]. (iii) The Hartree or the Hartree-Fock equations for many-electron systems.…”

Section: Introductionmentioning

confidence: 99%

On the variational principle for the non-linear Schrödinger equation

et al. 2019

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While variation of the energy functional yields the Schrödinger equation in the usual, linear case, no such statement can be formulated in the general nonlinear situation when the Hamiltonian depends on its eigenvector. In this latter case, as we illustrate by sample numerical calculations, the points of the energy expectation value hypersurface where the eigenvalue equation is satisfied separate from those where the energy is stationary. We show that the variation of the energy at the eigensolution is determined by a generalized Hellmann-Feynman theorem. Functionals, other than the energy, can, however be constructed, that result the nonlinear Schrödinger equation upon setting their variation zero. The second centralized moment of the Hamiltonian is one example.

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A variational principle for coupled nonlinear Schrödinger equations with variable coefficients and high nonlinearity

Cited by 14 publications

References 22 publications

Lagrangians of the (2+1) -dimensional KP equation with variable coefficients and cross terms

Lagrangians of the (2+1) -dimensional KP equation with variable coefficients and cross terms

A Note on the Semi-Inverse Method and a Variational Principle for the Generalized KdV-mKdV Equation

On the variational principle for the non-linear Schrödinger equation

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