Functional Separation of Variables in Nonlinear PDEs: General Approach, New Solutions of Diffusion-Type Equations
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- Andrei D. Polyanin, 2019. "Comparison of the Effectiveness of Different Methods for Constructing Exact Solutions to Nonlinear PDEs. Generalizations and New Solutions," Mathematics, MDPI, vol. 7(5), pages 1-19, April.
- Bradshaw-Hajek, B.H. & Moitsheki, R.J., 2015. "Symmetry solutions for reaction–diffusion equations with spatially dependent diffusivity," Applied Mathematics and Computation, Elsevier, vol. 254(C), pages 30-38.
- Polyanin, Andrei D., 2019. "Functional separable solutions of nonlinear reaction–diffusion equations with variable coefficients," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 282-292.
- Zhang, Shun-Li & Lou, S.Y., 2004. "Derivative-dependent functional separable solutions for the KdV-type equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 335(3), pages 430-444.
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- Andrei D. Polyanin & Vsevolod G. Sorokin, 2021. "Nonlinear Pantograph-Type Diffusion PDEs: Exact Solutions and the Principle of Analogy," Mathematics, MDPI, vol. 9(5), pages 1-22, March.
- Alexander V. Aksenov & Andrei D. Polyanin, 2021. "Methods for Constructing Complex Solutions of Nonlinear PDEs Using Simpler Solutions," Mathematics, MDPI, vol. 9(4), pages 1-31, February.
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Keywords
functional separation of variables; generalized separation of variables; exact solutions; nonlinear reaction-diffusion equations; nonlinear partial differential equations; equations of mathematical physics; splitting principle; nonclassical method of symmetry reductions; invariant surface condition; differential constraints;All these keywords.
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