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Functional analysis --- Differential equations, Nonlinear --- Nonlinear integral equations --- Numerical solutions. --- Functional analysis. --- Differential equations, Nonlinear - Numerical solutions. --- Nonlinear integral equations - Numerical solutions.

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Stochastic processes --- Partial differential equations --- Stochastic partial differential equations --- Differential equations, Nonlinear --- Convergence --- Numerical solutions --- Congresses. --- Probabilities --- Congresses --- Differential equations [Nonlinear ] --- Differential equations [Partial ] --- Stochastic partial differential equations - Numerical solutions - Congresses. --- Differential equations, Nonlinear - Numerical solutions - Congresses. --- Convergence - Congresses.

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As a partner to Volume 1: Dimensional Continuous Models, this monograph provides a self-contained introduction to algebro-geometric solutions of completely integrable, nonlinear, partial differential-difference equations, also known as soliton equations. The systems studied in this volume include the Toda lattice hierarchy, the Kac-van Moerbeke hierarchy, and the Ablowitz-Ladik hierarchy. An extensive treatment of the class of algebro-geometric solutions in the stationary as well as time-dependent contexts is provided. The theory presented includes trace formulas, algebro-geometric initial value problems, Baker-Akhiezer functions, and theta function representations of all relevant quantities involved. The book uses basic techniques from the theory of difference equations and spectral analysis, some elements of algebraic geometry and especially, the theory of compact Riemann surfaces. The presentation is constructive and rigorous, with ample background material provided in various appendices. Detailed notes for each chapter, together with an exhaustive bibliography, enhance understanding of the main results.

Differential equations, Nonlinear --- Solitons --- Numerical solutions --- Solitons. --- Pulses, Solitary wave --- Solitary wave pulses --- Wave pulses, Solitary --- Connections (Mathematics) --- Nonlinear theories --- Wave-motion, Theory of --- Numerical analysis --- Numerical solutions. --- Differential equations, Nonlinear - Numerical solutions

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Partial differential equations --- Differential equations, Nonlinear --- Nonlinear mechanics --- Equations différentielles non linéaires --- Numerical solutions --- Mathematics --- Solutions numériques --- Basic Sciences. Mathematics --- Numerical solutions. --- Mathematics. --- Differential and Integral Equations --- Differential and Integral Equations. --- Equations différentielles non linéaires --- Solutions numériques --- Nonlinear mechanics - Mathematics --- Differential equations, Nonlinear - Numerical solutions

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Evolution equations, Nonlinear --- Differential equations, Nonlinear --- Mathematical physics --- Numerical solutions --- Congresses. --- Équations différentielles non linéaires --- Équations d'évolution non linéaires --- Physique mathématique. --- Solutions numériques. --- Evolution equations, Nonlinear - Numerical solutions - Congresses. --- Differential equations, Nonlinear - Numerical solutions - Congresses. --- Mathematical physics - Congresses. --- Numerical solutions. --- Équations différentielles non linéaires --- Équations d'évolution non linéaires --- Physique mathématique. --- Solutions numériques.