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Variational principles for some nonlinear partial differential equations with variable coefficients. (English) Zbl 1135.35303
The author suggests a method to search for various variational principles for physical problems. The most interesting features of the proposed method, compared with Noether’s theorem, are its extreme simplicity and concise results for a wide range of nonlinear problems.

35A15Variational methods (PDE)
35Q53KdV-like (Korteweg-de Vries) equations
35Q55NLS-like (nonlinear Schrödinger) equations
37K10Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies
Full Text: DOI
[1] Liu, G. L.: A new finite element with self-adapting built-in discontinuity for shock-capturing in transonic flow. Int. J. Nonlinear sci. Numer. simul. 1, No. 1, 25-30 (2000) · Zbl 1005.76058
[2] Khater, A. H.; Moussa, M. H. M.; Abdul-Aziz, S. F.: Invariant variational principles and conservation laws for some nonlinear partial differential equations with constant coefficients--II. Chaos, solitons & fractals 15, 1-13 (2003) · Zbl 1032.35018
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[4] He, J. H.: A classical variational model for micropolar elastodynamics. Int. J. Nonlinear sci. Numer. simul. 1, No. 2, 133-138 (2000) · Zbl 0967.74008
[5] He, J. H.: Hamilton principle and generalized variational principles of linear thermopiezoelectricity. ASME J. Appl. mech. 68, No. 4, 666-667 (2001) · Zbl 1110.74474
[6] He, J. H.: Variational theory for linear magneto-electro-elasticity. Int. J. Nonlinear sci. Numer. simul. 2, No. 4, 309-316 (2001) · Zbl 1083.74526
[7] Mosconi, M.: Mixed variational formulations for continua with microstructure. Int. J. Solids struct. 39, 4181-4195 (2002) · Zbl 1032.74009
[8] Hui, S.; Mingfu, F.: Semi-inverse method of generalized variational inequalities in elasticity with finite displacement and friction. Chinese J. Mech. eng. 37, No. 8, 12-17 (2001)
[9] Hao, T. H.: Application of the Lagrange multiplier method the semi-inverse method to the search for generalized variational principle in quantum mechanics. Int. J. Nonlinear sci. Numer. simul. 4, No. 3, 311-312 (2003)