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[null,"1.","Record Nr.",null,"UNINA9910829176903321"]
[null,null,"Titolo",null,"The dynamics of modulated wave trains / / Arjen Doelman [and three others]"]
[null,null,"Pubbl/distr/stampa",null,"Providence, Rhode Island : , : American Mathematical Society, , 2009"]
[{"$nulls":4},"©2009"]
[null,null,"ISBN",null,"1-4704-0540-7"]
[null,null,"Descrizione fisica",null,"1 online resource (122 p.)"]
[null,null,"Collana",null,"Memoirs of the American Mathematical Society, , 0065-9266 ; ; Volume 199, Number 934"]
[null,null,"Disciplina",null,"515.3534"]
[null,null,"Soggetti",null,"Reaction-diffusion equations"]
[{"$nulls":4},"Approximation theory"]
[{"$nulls":4},"Burgers equation"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Note generali","\"Volume 199, Number 934 (fifth of 6 numbers).\""]
[null,null,null,"Nota di bibliografia","Includes bibliographical references."]
[null,null,"Nota di contenuto",null,"\"\"Contents\"\"; \"\"Notation\"\"; \"\"Chapter 1. Introduction\"\"; \"\"1.1. Grasshopper's guide\"\"; \"\"1.2. Slowly-varying modulations of nonlinear wave trains\"\"; \"\"1.3. Predictions from the Burgers equation\"\"; \"\"1.4. Verifying the predictions made from the Burgers equation\"\"; \"\"1.5. Related modulation equations\"\"; \"\"1.6. References to related works\"\"; \"\"Chapter 2. The Burgers equation\"\"; \"\"2.1. Decay estimates\"\"; \"\"2.2. Fronts in the Burgers equation\"\"; \"\"Chapter 3. The complex cubic Ginzburgâ€?Landau equation\"\"; \"\"3.1. Set-up\"\"; \"\"3.2. Slowly-varying modulations of the k = 0 wave train: Results\"\""]
[{"$nulls":4},"\"\"3.3. Derivation of the Burgers equation\"\"\"\"3.4. The construction of higher-order approximations\"\"; \"\"3.5. The approximation theorem for the wave numbers\"\"; \"\"3.6. Mode filters, and separation into critical and noncritical modes\"\"; \"\"3.7. Estimates of the linear semigroups\"\"; \"\"3.8. Estimates of the residual\"\"; \"\"3.9. Estimates of the errors\"\"; \"\"3.10. Proofs of the theorems from Â3.2\"\"; \"\"Chapter 4. Reaction-diffusion equations: Set-up and results\"\"; \"\"4.1. The abstract set-up\"\"; \"\"4.2. Expansions of the linear and nonlinear dispersion relations\"\""]
[{"$nulls":4},"\"\"4.3. Formal derivation of the Burgers equation\"\"\"\"4.4. Validity of the Burgers equation\"\"; \"\"4.5. Existence and stability of weak shocks\"\"; \"\"Chapter 5. Validity of the Burgers equation in reaction-diffusion equations\"\"; \"\"5.1. From phases to wave numbers\"\"; \"\"5.2. Bloch-wave analysis\"\"; \"\"5.3. Mode filters, and separation into critical and noncritical modes\"\"; \"\"5.4. Estimates for residuals and errors\"\"; \"\"5.5. "]
[{"$nulls":4},"Proofs of the theorems from Â4.4\"\"; \"\"Chapter 6. Validity of the inviscid Burgers equation in reaction-diffusion systems\"\"; \"\"6.1. An illustration: The Ginzburgâ€?Landau equation\"\""]
[{"$nulls":4},"\"\"6.2. Formal derivation of the conservation law\"\"\"\"6.3. Validity of the inviscid Burgers equation\"\"; \"\"6.4. Proof of the theorems from Â6.3\"\"; \"\"Chapter 7. Modulations of wave trains near sideband instabilities\"\"; \"\"7.1. Introduction\"\"; \"\"7.2. An illustration: The Ginzburgâ€?Landau equation\"\"; \"\"7.3. Validity of the Kortewegâ€?de Vries and the Kuramotoâ€?Sivashinsky equation\"\"; \"\"7.4. Proof of Theorem 7.2\"\"; \"\"7.5. Proof of Theorem 7.5\"\"; \"\"Chapter 8. Existence and stability of weak shocks\"\"; \"\"8.1. Proof of Theorem 4.10\"\"; \"\"8.2. Proof of Theorem 4.12\"\""]
[{"$nulls":4},"\"\"Chapter 9. Existence of shocks in the long-wavelength limit\"\"\"\"9.1. A lattice model for weakly interacting pulses\"\"; \"\"9.2. Proof of Theorem 9.2\"\"; \"\"Chapter 10. Applications\"\"; \"\"10.1. The FitzHughâ€?Nagumo equation\"\"; \"\"10.2. The weakly unstable Taylorâ€?Couette problem\"\"; \"\"Bibliography\"\""]