Results 11 to 20 of about 3,164,214 (296)
Results in Physics, 2023 In this paper the system of equations arising from a simplified micromorphic model is studied using the Lie symmetry approach. The advantage of this approach is that is provides exact invariant solutions rather than numerical or approximate ones reported
M. Usman +3 more
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Group Invariant Solutions Without Transversality [PDF]
Communications in Mathematical Physics, 2000 We present a generalization of Lie's method for finding the group invariant solutions to a system of partial differential equations. Our generalization relaxes the standard transversality assumption and encompasses the common situation where the reduced differential equations for the group invariant solutions involve both fewer dependent and ...
Anderson, Ian M. +2 more
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Invariant Solutions for Nonhomogeneous Discrete Diffusion Equation [PDF]
Discrete Dynamics in Nature and Society, 2013 One-dimensional optimal systems for nonhomogeneous discrete heat equation with different source terms are calculated. By utilizing these optimal systems invariant solutions are found.
M. N. Qureshi +3 more
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Negatively Invariant Sets and Entire Solutions [PDF]
Journal of Dynamics and Differential Equations, 2010 Negatively invariant compact sets of autonomous and nonautonomous dynamical systems on a metric space, the latter formulated in terms of processes, are shown to contain a strictly invariant set and hence entire solutions. For completeness the positively invariant case is also considered. Both discrete and continuous time systems are considered.
Kloeden, Peter E., Marín Rubio, Pedro
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Invariant Solutions and Conservation Laws of the (2 + 1)-Dimensional Boussinesq Equation [PDF]
Abstract and Applied Analysis, 2014 Invariant solutions and conservation laws of the (2 + 1)-dimensional Boussinesq equation are studied. The Lie symmetry approach is used to obtain the invariant solutions.
Wenjuan Rui, Peiyi Zhao, Yufeng Zhang
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Invariant Solutions for Soil Water Equations
Mathematical and Computational Applications, 1999 We obtain exact solutions for a class of nonlinear partial differential equations which models soil water infiltration and redistribution in a bedded soil profile irrigated by a drip irrigation system. The solutions obtained are invariant under two parameter symmetry groups.
Baikov, V., Khalique, C.
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Making solutions invariant [PDF]
International Journal of Game Theory, 2003 This paper presents a method to modify a non-invariant solution concept in such a way that the resulting solution is invariant. The properties of the solution which are inherited by the modified solution are also analyzed. In particular, the authors show that the modified solution concept inherits all other requirements of Kohlberg-Mertens program ...
Vermeulen, A.J. +2 more
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Lie symmetry analysis for generalized short pulse equation
Open Physics, 2022 Lie symmetry analysis (LSA) is one of the most common, effective, and estimation-free methods to find the symmetries and solutions of the differential equations (DEs) by following an algorithm.
Zhao Weidong +4 more
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Mathematics, 2020 On one hand, we construct λ-symmetries and their corresponding integrating factors and invariant solutions for two kinds of ordinary differential equations.
Yu-Shan Bai, Jian-Ting Pei, Wen-Xiu Ma
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Pracì Mìžnarodnogo Geometričnogo Centru, 2021 We study the relationship between structural properties of the two-dimensional nonconjugate subalgebras of the same rank of the Lie algebra of the Poincaré group P(1,4) and the properties of reduced equations for the (1+3)-dimensional homogeneous Monge ...
Vasyl Fedorchuk, Volodymyr Fedorchuk
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