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Partial Differential Equations of Mathematical Physics

• Polyanin, A. D. and Zhurov, A. I., The von Mises transformation: order reduction and construction of Bäcklund transformations and new integrable equations, EqWorld—The World of Mathematical Equations, 3 July 2009.
• Polyanin, A. D. and Zhurov, A. I., The Crocco transformation: order reduction and construction of Bäcklund transformations and new integrable equations, arXiv:0907.3170v1 [nlin.SI], 21 July 2009.
• Polyanin, A. D., Schiesser, W. E., and Zhurov, A. I., Partial differential equations (2008), Scholarpedia, 3(10):4605.
  • First-Order Partial Differential Equations
  • Second-Order Partial Differential Equations
  • Higher-Order Partial Differential Equations
  • Numerical Methods
• Hamdi, S., Schiesser, W. E., and Griffiths, G. W., Method of lines, (2007), Scholarpedia, 2(7):2859.
• Conte, R., Exact solutions of nonlinear partial differential equations by singularity analysis, CIME School, Cetraro, 5–12 September 1999.
• Kalnins, E. G. and Miller, W., Variable separation in mathematical physics: From intuitive concept to mathematical tool, 2004.
• Kosovtsov, Yu. N., The decomposition method and Maple procedure for finding first integrals of nonlinear PDEs of any order with any number of independent variables, arXiv:0704.0072v1 [math-ph], 2007.
• Nucci, M. C., Nonclassical symmetries as special solutions of heir-equations, arXiv:nlin.SI/0011008v2, 31 Aug 2003.
• Olver, P. J., and Vorob'ev, E. M., Nonclassical and conditional symmetries, In: CRC Handbook of Lie Group Analysis of Differential Equations, Vol. 3, N. H. Ibragimov, ed., CRC Press, Boca Raton, 1996, pp. 291–328.
• Polyanin, A. D., Lectures on solution methods for nonlinear partial differential equations of mathematical physics, 2004:
  • Method of Generalized Separation of Variables
  • Method of Functional Separation of Variables
  • Differential Constraints Method
• Svirshchevskii, S. R., Invariant Linear Spaces and Exact Solutions of Nonlinear Evolution Equations, J. Nonlinear Math. Physics, 1996, Vol. 3, No. 1-2, pp. 164-169.
• Teodorovich, E. V., The renormalization-group method in problems of mathematical physics, J. Appl. Maths Mechs, 2004, Vol. 68, No. 2, pp. 299-326.
• Tychynin, V., Petrova, O., and Tertyshnyk, O., Nonlocal symmetries and genaration of solutions for partial differential equations, arXiv:math-ph/0702033v1, 9 Feb 2007.