Invariant Solutions for a Class of Perturbed Nonlinear Wave Equations
Abstract
:1. Introduction
2. Perturbed Nonlinear (1 + 1)-Dimension Wave Equation
Approximate Invariant Solution
3. Perturbed Nonlinear (2 + 1)-Dimension Wave Equation
3.1. Exact Symmetries
3.2. Approximate Symmetries
3.3. Approximate Invariant Solutions
4. Nonlinear Wave Equation with a Forcing Term
4.1. Approximate Symmetries by Method I
4.2. Approximate Symmetries by Method II
4.3. Approximate Invariant Solution
5. Concluding Remarks
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Ahmed, W.A.; Zaman, F.D.; Saleh, K. Invariant Solutions for a Class of Perturbed Nonlinear Wave Equations. Mathematics 2017, 5, 59. https://doi.org/10.3390/math5040059
Ahmed WA, Zaman FD, Saleh K. Invariant Solutions for a Class of Perturbed Nonlinear Wave Equations. Mathematics. 2017; 5(4):59. https://doi.org/10.3390/math5040059
Chicago/Turabian StyleAhmed, Waheed A., F. D. Zaman, and Khairul Saleh. 2017. "Invariant Solutions for a Class of Perturbed Nonlinear Wave Equations" Mathematics 5, no. 4: 59. https://doi.org/10.3390/math5040059
APA StyleAhmed, W. A., Zaman, F. D., & Saleh, K. (2017). Invariant Solutions for a Class of Perturbed Nonlinear Wave Equations. Mathematics, 5(4), 59. https://doi.org/10.3390/math5040059