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| 001 | 666954 | ||
| 005 | 20231030042054.0 | ||
| 035 | _a(RuTPU)RU\TPU\network\38158 | ||
| 090 | _a666954 | ||
| 100 | _a20220208a2018 k y0engy50 ba | ||
| 101 | 0 | _aeng | |
| 102 | _aUS | ||
| 135 | _adrcn ---uucaa | ||
| 181 | 0 | _ai | |
| 182 | 0 | _ab | |
| 200 | 1 |
_aAn application of the Maslov complex germ method to the one-dimensional nonlocal Fisher–KPP equation _fA. V. Shapovalov, A. Yu. Trifonov |
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| 203 |
_aText _celectronic |
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| 300 | _aTitle screen | ||
| 330 | _aA semiclassical approximation approach based on the Maslov complex germ method is considered in detail for the one-dimensional nonlocal Fisher–Kolmogorov–Petrovskii–Piskunov (Fisher–KPP) equation under the supposition of weak diffusion. In terms of the semiclassical formalism developed, the original nonlinear equation is reduced to an associated linear partial differential equation and some algebraic equations for the coefficients of the linear equation with a given accuracy of the asymptotic parameter. The solutions of the nonlinear equation are constructed from the solutions of both the linear equation and the algebraic equations. The solutions of the linear problem are found with the use of symmetry operators. A countable family of the leading terms of the semiclassical asymptotics is constructed in explicit form. The semiclassical asymptotics are valid by construction in a finite time interval. We construct asymptotics which are different from the semiclassical ones and can describe evolution of the solutions of the Fisher–KPP equation at large times. In the example considered, an initial unimodal distribution becomes multimodal, which can be treated as an example of a space structure. | ||
| 333 | _aРежим доступа: по договору с организацией-держателем ресурса | ||
| 461 |
_tInternational Journal of Geometric Methods in Modern Physics _oScientific Journal |
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| 463 |
_tVol. 15, iss. 6 _v[1850102, 28 p.] _d2018 |
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| 610 | 1 | _aэлектронный ресурс | |
| 610 | 1 | _aтруды учёных ТПУ | |
| 610 | 1 | _aNonlocal Fisher | |
| 610 | 1 | _aKPP equation | |
| 610 | 1 | _asemiclassical approximation | |
| 610 | 1 | _acomplex germ | |
| 610 | 1 | _asymmetry operators | |
| 610 | 1 | _apattern formation | |
| 700 | 1 |
_aShapovalov _bA. V. _cmathematician _cProfessor of Tomsk Polytechnic University, Doctor of physical and mathematical sciences _f1949- _gAleksandr Vasilyevich _2stltpush _3(RuTPU)RU\TPU\pers\31734 |
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| 701 | 1 |
_aTrifonov _bA. Yu. _cphysicist, mathematician _cProfessor of Tomsk Polytechnic University, Doctor of physical and mathematical sciences _f1963- _gAndrey Yurievich _2stltpush _3(RuTPU)RU\TPU\pers\30754 |
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| 712 | 0 | 2 |
_aНациональный исследовательский Томский политехнический университет _bИсследовательская школа физики высокоэнергетических процессов _c(2017- ) _h8118 _2stltpush _3(RuTPU)RU\TPU\col\23551 |
| 801 | 2 |
_aRU _b63413507 _c20220208 _gRCR |
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| 856 | 4 | _uhttps://doi.org/10.1142/S0219887818501025 | |
| 942 | _cCF | ||