Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Conjugate gradient method for finding fundamental solitary waves   The Conjugate Gradient method (CGM) is known to be the fastest generic
iterative method for solving linear systems with symmetric sign definite
matrices. In this paper, we modify this method so that it could find
fundamental solitary waves of nonlinear Hamiltonian equations. The main
obstacle that such a modified CGM overcomes is that the operator of the
equation linearized about a solitary wave is not sign definite. Instead, it has
a finite number of eigenvalues on the opposite side of zero than the rest of
its spectrum. We present versions of the modified CGM that can find solitary
waves with prescribed values of either the propagation constant or power. We
also extend these methods to handle multi-component nonlinear wave equations.
Convergence conditions of the proposed methods are given, and their practical
implications are discussed. We demonstrate that our modified CGMs converge much
faster than, say, Petviashvili's or similar methods, especially when the latter
converge slowly.

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The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
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The categories of this paper are: atom-ph
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
2
The categories of this paper are: math
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The categories of this paper are: supr-con
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The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: stat
0
The categories of this paper are: hep-ph
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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
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The categories of this paper are: eess