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Discrete and Continuous Dynamical Systems - Series S (DCDS-S)
 

Conservation laws and symmetries of time-dependent generalized KdV equations
Pages: 607 - 615, Issue 4, August 2018

doi:10.3934/dcdss.2018035      Abstract        References        Full text (335.1K)           Related Articles

Stephen Anco - Department of Mathematics and Statistics, Brock University, St. Catharines, Canada (email)
María Rosa - Dpto. de Matemáticas, Universidad de Cádiz, Polígono del Río San Pedro s/n 11510 Puerto Real, Cádiz, Spain (email)
Maria Luz Gandarias - Departamento de Matemáticas, Universidad de Cádiz , Polígono del Río San Pedro s/n 11510 Puerto Real, Cádiz, Spain (email)

1 S. C. Anco and G. Bluman, Direct Construction of Conservation Laws from Field Equations, Phys. Rev. Lett., 78 (1997), 2869-2873.       
2 S. C. Anco and G. Bluman, Direct construction method for conservation laws of partial differential equations II: General treatment, Euro. J. Appl. Math., 13 (2002), 567-585.       
3 S. C. Anco, Generalization of Noether's theorem in modern form to non-variational partial differential equations, in Recent progress and Modern Challenges in Applied Mathematics, Modeling and Computational Science, 119-182, Fields Institute Communications, 79, 2017.
4 S. C. Anco and M. L. Gandarias, Conservation laws and symmetries of a class of dispersive semilinear wave equations, in preparation, 2017.
5 S. C. Anco and G. Bluman, Direct construction method for conservation laws of partial differential equations I: Examples of conservation law classifications, Euro. Jour. Appl. Math., 13 (2002), 545-566.       
6 I. Bakirtas and H. Demiray, Weakly nonlinear waves in a tapered elastic tube filled with an inviscid fluid, Int. J. Nonlinear Mech., 40 (2005), 785-793.       
7 G. W. Bluman, A Cheviakov and S. C. Anco, Applications of Symmetry Methods to Partial Differential Equations, New York: Springer, 2010.       
8 R. C. Cascaval, Variable coefficient KdV equations and waves in elastic tubes, in Evolution Equations (eds. G.R. Goldstein, R. Nagel, S. Romanelli), 57-69, Lecture Notes in Pure and Appl. Math., 234, Dekker, New York, 2003.       
9 H. Demiray, The effect of a bump on wave propagation in a fluid-filled elastic tube, Int. J. Eng. Sci., 42 (2004), 203-215; ibid, Weakly nonlinear waves in a linearly tapered elastic tube filled with a fluid, Math. Comput. Mod., 39 (2004), 151-162.       
10 A. G. Johnpillai, C. M. Khalique and A. Biswas, Exact solutions of KdV equation with time-dependent coefficients, Applied Mathematics and Computation, 216 (2010), 3114-3119.       
11 T. Kakutani and H. Ono, J. Phys. Soc. Jpn., 26 (1969), 1305-1318.
12 W.-X. Ma, R. K. Bullough, P. J. Caudrey and W. I. Fushchych, Time-dependent symmetries of variable-coefficient evolution equations and graded Lie algebras, J. Phys. A: Math. Gen., 30 (1997), 5141-5149.       
13 W.-X. Ma and R. Zhou, Adjoint symmetry constraints leading to binary nonlinearization, J. Nonlin. Math. Phys., 9 (2002), 106-126.       
14 M. Moulati and C. M. Khalique, Group analysis of a generalized KdV equation, Appl. Math. Inf. Sci., 8 (2014), 2845-2848.       
15 V. Narayanamurti and C. M. Varma, Nonlinear propagation of heat pulses in solids, Phys. Rev. Lett., 25 (1970), 1105-1108.
16 P. J. Olver, Applications of Lie Groups to Differential Equations, Berlin: Springer, 1986.       
17 R. O. Popovych and A. Sergyeyev, Conservation laws and normal forms of evolution equations, Phys. Lett. A, 374 (2010), 2210-2217.       
18 F. D. Tappert and C. M. Varma, Asymptotic theory of self-trapping of heat pulses in solids, Phys. Rev. Lett., 25 (1970), 1108-1111.       
19 M. Wadati, Wave propagation in nonlinear lattice, J. Phys. Soc. Japan, 38 (1975), 673-680.       
20 N. J. Zabusky, A synergetic approach to problems of nonlinear dispersive wave propagation and interaction, in Proc. Symp. Nonlinear Partial Differential Equations (ed. W. Ames), 223-258, Academic Press, 1967.

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