Advances in Nonlinear Waves and Symbolic Computation.

Intro -- Advances in Nonlinear Waves and Symbolic Computation -- Contents -- Preface -- Chirped Optical Solitons -- Abstract -- 1. Introduction -- 2. Theoretical Model -- 3. Chirped Optical Soliton: Hirota Bilinear Method -- 4. Physical Explanation of Chirped Optical Soliton: Variational Analysis -- 5. Pulse Compression in Terms of Chirped Soliton -- 6. Chirped Higher Order Solitons -- 7. Studies on Chirped Higher Order Solitons -- 8. Conclusion -- Acknowledgement -- References -- Direct Methods and Symbolic Software for Conservation Laws of Nonlinear Equations -- Abstract -- 1. Introduction -- Part I: Partial Differential Equations in (1 + 1) Dimensions -- 2. The Most Famous Example in Historical Perspective -- 3. The Method of Undetermined Coefficients -- 4. Tools from the Calculus of Variations and Differential Geometry -- 5. Conservation Laws of Nonlinear Systems of Polynomial PDEs -- 6. Conservation Laws of Systems of PDEs with Transcendental Nonlinearities -- 7. Conservation Laws of Scalar Equations with Transcendental and Mixed Derivative Terms -- Part II: Nonlinear Differential-Difference Equations -- 8. Nonlinear DDEs and Conservation Laws -- 9. The Method of Undetermined Coefficients for DDEs -- 10. Discrete Euler and Homotopy Operators -- 11. Conservation Laws of Nonlinear Systems of DDEs -- 12. A New Method to Compute Conservation Laws of Nonlinear DDEs -- 13. The Gardner Lattice -- 14. Additional Examples of Nonlinear DDEs -- 15. Software to Compute Conservation Laws for PDEs and DDEs -- 16. Summary -- Acknowledgements -- References -- Nonclassical Potential Symmetries for a Nonlinear Thermal Wave Equation -- Abstract -- 1. Introduction -- 2. Nonclassical Potential Symmetries for the Nonlinear Thermal Wave Equation -- 3. Nonclassical Symmetries and Nonclassical Potential Symmetries for the Fokker-Planck Equation.

4. Concluding Remarks -- Acknowledgements -- References -- Anti-Dark Solitons of the Resonant Nonlinear Schrodinger Equation -- Abstract -- 1. Introduction -- 2. Bilinear Form of the Resonant Nonlinear Schrodinger Equation -- 3. Soliton Solutions -- 4. Periodic Wave Solutions -- 5. Conclusions -- Acknowledgement -- References -- Similarity Solutions for the Boiti-Leon-Pempinelli Equation with Symbolic Computation -- Abstract -- 1. Introduction -- 2. Symmetry Reductions for the BLP Equation -- 3. Similarity Solutions -- 4. Maple Implementation of the Further Extended Tanh Method -- 5. Conclusion and Discussion -- References -- The New Sine-Gordon Expansion Algorithms to Construct Exact Solutions of Nonlinear Wave Equations -- Abstract -- 1. Introduction and Proposition -- 2. The New Sine-Gordon Equation Expansion Algorithm -- 3. The Applications of Algorithm I -- 4. The Application of Algorithm II -- 5. Conclusions -- Acknowledgement -- References -- Index.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.