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Method of Invariant Grids
The method of invariant grids is developed for a grid-based computation of invariant manifolds.
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Mathematical Notation and Some Terminology
– The operator L from space W to space E: L : W → E
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Invariance Equation in Differential Form
Definition of invariance in terms of motions and trajectories assumes, at least, existence and uniqueness theorems for solutions of the original...
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Entropy, Quasiequilibrium, and Projectors Field
Projection operators Py contribute both to the invariance equation (3.2), and to the film extension of the dynamics (4.5). Limiting results, exact...
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Results for Sr2RuO4
In this chapter, we focus on our results for the elementary excitations and Cooper pairing in strontium ruthenate (...
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Nonlinear superposition formulae of integrable partial differential equations by the singular manifold method
We study by the singular manifold method a few 1+1-dimensional partial differential equations which possess N-soliton solutions for arbitrary N, i.e....
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Theory of Cooper Pairing Due to Exchange of Spin Fluctuations
It is of general interest whether singlet high- \(T_{\rm c}\)...
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Nonlinear Waves, Solitons, and IST
These lectures are written for a wide audience with diverse backgrounds. The subject is approached from a general perspective and overly detailed...
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Integrability – and How to Detect It
We present a physicist’s approach to integrability and its detection. Starting from specific examples we present a working definition of what is...
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Bilinear Formalism in Soliton Theory
A brief survey of the bilinear formalism discovered by Hirota is given. First, the procedure to obtain soliton solutions of nonlinear evolution...
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Extremal Properties of Random Structures
The extremal characteristics of random structures, including trees, graphs, and networks, are discussed. A statistical physics approach is employed...
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On the Analysis of Backtrack Proceduresfor the Colouring of Random Graphs
Backtrack search algorithms are procedures capable of deciding whether a decision problem has a solution or not through a sequence of trials and...
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Attacks and Cascades in Complex Networks
This paper reviews two problems in the security of complex networks: cascades of overload failures on nodes and range-based attacks on links....
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Tomography and Stability of Complex Networks
We study the structure of generalized random graphs with a given degree distribution P(k), and review studies on their behavior under both random...
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Topology, Hierarchy, and Correlations in Internet Graphs
We present a statistical analysis of different metrics characterizing the topological properties of Internet maps, collected at two different...
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The Small World Phenomenonin Hybrid Power Law Graphs
The small world phenomenon, that consistently occurs in numerous existing networks, refers to two similar but different properties — small average...
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Introduction
Nonlinear systems model all but the simplest physical phenomena. In the classical theory, the tools of Poisson geometry appear in an essential way,...
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Critical Phenomena in a Small World
We consider the behavior of various systems on a small-world network near a critical point. Our starting point is a different, nonrandom system with...
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Who Is the Best Connected Scientist?A Study of Scientific Coauthorship Networks
Using data from computer databases of scientific papers in physics, biomedical research, and computer science, we have constructed networks of...