Camasa-Holm方程
￥ 128 7.6折 ￥ 168 九五品
仅1件
北京东城
认证卖家担保交易快速发货售后保障
作者郭柏灵,殷朝阳,杨灵娥,吴兴龙
出版社科学出版社
ISBN9787030595577
出版时间2022-03
版次1
装帧精装
开本16开
纸张胶版纸
页数287页
定价168元
上书时间2024-03-28
商品详情
- 品相描述：九五品
- 商品描述
-
基本信息
书名:Camasa-Holm方程
定价：168.00元
作者:郭柏灵,殷朝阳,杨灵娥,吴兴龙
出版社：科学出版社
出版日期：2022-03-01
ISBN：9787030595577
字数：
页码：287
版次：
装帧：精装
开本：16开
商品重量：
编辑推荐
内容提要
Camassa-Holm方程是一类十分重要而又特别的新型浅水波方程，有广泛的应用背景。该类方程存在一类尖峰孤立子，并且它是完全可积的,具有双哈密顿结构和Lax对。《Camassa-Holm方程》给出该类方程的物理背景并阐述它的完全可积性。对该类方程的行波解作分类，获得多种奇异孤立波解；给出该类方程的谱图理论和散射数据；利用反散射方法，给出该类方程的多孤立子解。获得该类方程的整体强解的存在性及整体弱解的存在性；得到该类方程柯西问题的局部适定性；研究它们的blow-up问题以及尖峰孤立子解的轨道稳定性。《Camassa-Holm方程》同时研究含尖峰孤立子的Degasperis-Procesi方程及b族方程，研究前一类方程激波的形成及动力学分析，给出b族方程的水波结构和非线性平衡关系，对Degasperis-Procesi方程的适定性给出具体证明。
目录
Contents Chapter 1 Physical Backgrounds and Complete Integrability of the Camassa-Holm Equatio1 1.1 Physical backgrounds of the Camassa-Holm equatio1 1.2 The complete integrability of the Camassa-Holm equatio9 1.3 Experimental observatioand applications of solitons 17 References 18 Chapter 2 Traveling Wave Solutions of the Camassa-Holm Equatio33 2.1 Introductio33 2.2 Notations 34 2.3 Weak form 36 2.4 Several types of traveling wave solutions 37 2.5 The proof Theorem 2.4.1 43 2.6 The correlatioof parameters 59 2.7 Wave length 63 2.8 Explicit formulae of peako66 References 68 Chapter 3 The Scattering and Inverse Scattering of the Camassa-Holm Equatio71 3.1 Scattering of the Camassa-Holm equatio71 3.1.1 Introductio71 3.1.2 Spectral graph theory 72 3.1.3 The scattering problem 82 3.2 The solutions of Camassa-Holm equatio89 3.2.1 Introductio89 3.2.2 Summary of the process 89 3.2.3 Summary of solving process 93 3.2.4 Solitary wave solutions 93 3.2.5 2-solitosolutions 97 3.2.6 Examples and properties of 2-solitosolutions 102 3.2.7 3-solitosolutions 106 3.2.8 Summary 109 References 111 Chapter 4 Well-posedness of the Camassa-Holm Equatio113 4.1 Global existence of strong solutions 113 4.1.1 The existence of local solutions 113 4.1.2 The existence of global solutions 120 4.2 The existence of global weak solutions 128 4.3 The local well posedness of the Cauchy problem to the Camassa-Holm equatioiHs (s > 2/3) 138 4.4 Blow-up phenomena of the Camassa-Holm equatio145 4.5 The orbital stability of peakosolutions 153 References 157 Chapter 5 Formatioand Dynamics Analysis of Shock Wave of the Degasperis-Procesi Equatio159 5.1 Introductio159 5.1.1 Peakons 159 5.1.2 Generalized weak solutions 162 5.2 The shock wave of the DP equatio164 5.3 Peakon， anti-peakoand the formatioof shock waves 172 5.4 Shock wave dynamics 184 5.5 Concluding remarks 190 References 191 Chapter 6 Water Wave Structure and Nonlinear Equilibrium of 6-Family Nonlinear Shallow Water Wave Equatio194 6.1 Introductio195 6.1.1 6-family shallow water wave equatio195 6.1.2 Outline of the paper 196 6.2 History and general properties of the 6-equatio197 6.2.1 Discrete symmetries: reversibility， parity， and signature 199 6.2.2 Lagrangiarepresentatio199 6.2.3 Preservatioof the norm ||m||L1/b， 0≤b≤1 200 6.2.4 Lagrangiarepresentatiofor integer b 201 6.2.5 Reversibility and Galileacovariance 202 6.2.6 Integral momentum conservatio202 6.3 Traveling waves and generalized functions 203 6.3.1 The case of b = 0 203 6.3.2 The case of b ≠ 0 205 6.3.3 The case of b > 0 206 6.3.4 The case of b 6.4 Pulsointeractions for b > 0 214 6.4.1 Pulsointeractions for b = 2 215 6.4.2 Peakointeractions for b = 2 and b = 3: numerical results 215 6.4.3 Pulson-pulsointeractions for b > 0 and symmetric g 217 6.4.4 Pulson-antipulsointeractions for b> 1 and symmetric g 220 6.4.5 Specializing pulsons to peakons for b = 2 and b = 3 222 6.5 Peakons of width a for arbitrary b 223 6.5.1 The slope dynamics of peakons: inflectiopoints and the steepening lemma whe1 6.5.2 The case of 0≤b≤1 226 6.6 Adding viscosity to peakodynamics 226 6.6.1 Burgers-a^ equation: analytical estimates 228 6.6.2 The traveling waves of Burgers-αβ equatiofor P(3 - b) = 1 and v = 0 230 6.7 The peakons under (6.1.1) adding viscosity and evolutioof (6.1.2) Burgers-αβ 231 6.7.1 The fate of peakons under adding viscosity 231 6.7.2 The fate of peakons under Burgers-ap evolutio238 6.8 Numerical results for peakoscattering and initial value problems 241 6.8.1 Peakoinitial value problems 241 6.8.2 Descriptioof our numerical methods 243 6.9 Conclusions 245 References 247 Chapter 7 The Degasperis-Procesi Equatio249 7.1 Introductio249 7.2 Local well-posedness 253 7.3 Blow up 255 7.4 Global strong solutions 259 7.5 Global weak solutions 263 7.6 Recent results and problems 278 References 284
作者介绍
序言
-
【封面】
相关推荐
— 没有更多了 —
以下为对购买帮助不大的评价