共查询到20条相似文献,搜索用时 15 毫秒
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Josef Kreulich 《Journal of Evolution Equations》2014,14(4-5):969-1000
We show how the approach of Yosida Approximation of the derivative serves to obtain new results for evolution systems. We give criteria for the asymptotic equivalence of two different evolution systems, i.e., $$\lim_{t \to \infty} \|U_A(t, s)x - U_B(t, s)x\| =0,$$ where the evolution systems are generated by two different families of nonlinear and multivalued time-dependent operators A(t), and B(t). 相似文献
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Commutator identities on associative algebras and the integrability of nonlinear evolution equations
A. K. Pogrebkov 《Theoretical and Mathematical Physics》2008,154(3):405-417
We show that commutator identities on associative algebras generate solutions of the linearized versions of integrable equations.
In addition, we introduce a special dressing procedure in a class of integral operators that allows deriving both the nonlinear
integrable equation itself and its Lax pair from such a commutator identity. The problem of constructing new integrable nonlinear
evolution equations thus reduces to the problem of constructing commutator identities on associative algebras.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 154, No. 3, pp. 477–491, March, 2008. 相似文献
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Translated from Sibirskii Matematicheskii, Vol. 36, No. 1, pp. 164–176, January–February, 1995. 相似文献
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Annika Lang 《Journal of Computational and Applied Mathematics》2010,234(12):3387-3396
In this paper, a stochastic mean square version of Lax’s equivalence theorem for Hilbert space valued stochastic differential equations with additive and multiplicative noise is proved. Definitions for consistency, stability, and convergence in mean square of an approximation of a stochastic differential equation are given and it is shown that these notions imply similar results as those known for approximations of deterministic partial differential equations. Examples show that the assumptions made are met by standard approximations. 相似文献
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William D. L. Appling 《Annali di Matematica Pura ed Applicata》1972,93(1):247-262
Summary A class of continuous functions is characterized in terms of integrability and integral equivalence.
Entrata in Redazione il 28 giugno 1971. 相似文献
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An algorithm is presented to prove the Painlevé integrability of parameterized nonlinear evolution equations such that one can filter out Painlevé integrable models from nonlinear equations with general forms. Then two well known nonlinear models with physical interests illustrate the effectiveness of this algorithm. Some new results are reported for the first time. 相似文献
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We consider the propagation of electromagnetic pulses in isotropic media taking a third-order nonlinearity into account. We develop a method for transforming Maxwell’s equations based on a complete set of projection operators corresponding to wave-dispersion branches (in a waveguide or in matter) with the propagation direction taken into account. The most important result of applying the method is a system of equations describing the one-dimensional dynamics of pulses propagating in opposite directions without accounting for dispersion. We derive the corresponding self-action equations. We thus introduce dispersion in the media and show how the operators change. We obtain generalized Schäfer-Wayne short-pulse equations accounting for both propagation directions. In the three-dimensional problem, we focus on optic fibers with dispersive matter, deriving and numerically solving equations of the waveguide-mode interaction. We discuss the effects of the interaction of unidirectional pulses. For the coupled nonlinear Schrödinger equations, we discuss a concept of numerical integrability and apply the developed calculation schemes. 相似文献
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In this paper after having obtained the Lax pair of a hierarchy of soliton equations,we discuss the parametric representation for finite-band solutions of the stationary solitonequation, and prove it can be represented as a Hamiltonian system which is integrable inLiouville sense. The nonconfocal involutive integral representations {Fm} are obtained also.In the condition of finite-band solutions of the soliton equation, the time and space can bedevided inio two Hamiltonian systems, so the fi… 相似文献
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One gives the Lax representation for Benney's longwave equations. One constructs the “universal conserved densities.” 相似文献
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I. T. Khabibullin 《Theoretical and Mathematical Physics》1993,96(1):845-853
Infinite series of local boundary conditions completely compatible with the inverse scattering method are presented for the nonlinear Schrödinger equation and the sine—Gordon equation.Institute of Mathematics with Computing Center, Urals Branch of the Russian Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 96, No. 1, pp. 109–122, July, 1993. 相似文献
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《Communications in Nonlinear Science & Numerical Simulation》2014,19(1):19-28
The equivalence of multilinear variable separation approach, the extended projective Ricatti equation method and the improved tanh-function method is firstly reported when these three popular methods are used to realize variable separation for nonlinear evolution equations. We take the (2 + 1)-dimensional modified Broer–Kaup system for an example to illustrate this point. All solutions obtained by the extended projective Ricatti equation method and the improved tanh-function method coincide with the one obtained by the multilinear variable separation approach. Moreover, based on one of variable separation solutions, we also find that although abundant localized coherent structures can be constructed for a special component, we must pay our attention to the solution expression of the corresponding other component for the same equation lest many un-physical related structures might be obtained. 相似文献
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