Advances in nonlinear waves and symbolic computation / / Zhenya Yan

• Record Nr.: UNINA9910956156003321
• Autore: Yan Zhenya
• Pubbl/distr/stampa: New York, : Nova Science Publishers, c2009
• ISBN: 1-60876-607-1
• Edizione: [1st ed.]
• Descrizione fisica: 1 online resource (162 p.)
• Disciplina: 531/.1133
• Soggetti: Nonlinear waves - Mathematical models; Solitons - Mathematical models; Nonlinear difference equations; Differential equations, Nonlinear
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Errata slip inserted.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: 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.
• Sommario/riassunto: With the rapid development of science and technology, the computer has become an important tool in many science fields. Particularly, symbolic computation, which is one of the most exciting and challenging areas. It has been applied in many sciences such as mathematics, physics, chemistry, biology, mechanics, engineering, etc., in particular, non-linear sciences ad complex sciences. Nowadays, many symbolic computation softwares have been used to deal with these problems. Up to now, there have existed many non-linear differential/difference systems related to solitons and chaos in the non-linear science field.In order to understand these complex physical phenomena, it is important to research some of their basic properties. Because of the complexity of these non-linear systems, with the symbolic computation, this new book presents important research on non-linear differential/difference systems, related to solitons and chaos as well as other non-linear sciences in views of constructive algorithms.