LEADER 05655nam 2200613Ia 450 001 9910956156003321 005 20251116181615.0 010 $a1-60876-607-1 035 $a(CKB)2550000001041355 035 $a(EBL)3018495 035 $a(SSID)ssj0000834838 035 $a(PQKBManifestationID)11526160 035 $a(PQKBTitleCode)TC0000834838 035 $a(PQKBWorkID)10981629 035 $a(PQKB)11398126 035 $a(MiAaPQ)EBC3018495 035 $a(Au-PeEL)EBL3018495 035 $a(CaPaEBR)ebr10660356 035 $a(OCoLC)853455918 035 $a(BIP)23908835 035 $a(EXLCZ)992550000001041355 100 $a20081017d2009 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aAdvances in nonlinear waves and symbolic computation /$fZhenya Yan 205 $a1st ed. 210 $aNew York $cNova Science Publishers$dc2009 215 $a1 online resource (162 p.) 300 $aErrata slip inserted. 311 08$a1-60692-260-2 320 $aIncludes bibliographical references and index. 327 $aIntro -- 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. 327 $a4. 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. 330 $aWith 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. 606 $aNonlinear waves$xMathematical models 606 $aSolitons$xMathematical models 606 $aNonlinear difference equations 606 $aDifferential equations, Nonlinear 615 0$aNonlinear waves$xMathematical models. 615 0$aSolitons$xMathematical models. 615 0$aNonlinear difference equations. 615 0$aDifferential equations, Nonlinear. 676 $a531/.1133 700 $aYan$b Zhenya$01866130 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910956156003321 996 $aAdvances in nonlinear waves and symbolic computation$94473428 997 $aUNINA