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Zh. Vychisl. Mat. Mat. Fiz., 2008, Volume 48, Number 5, Pages 808–812 (Mi zvmmf138)  

This article is cited in 11 scientific papers (total in 11 papers)

Traveling-wave solution to a nonlinear equation in semiconductors with strong spatial dispersion

A. B. Alshin, M. O. Korpusov, E. V. Yushkov

Faculty of Physics, Moscow State University, Leninskie gory, Moscow, 119992, Russia

Abstract: The third-order nonlinear differential equation $(u_{xx}-u)_t+u_{xxx}+uu_x=0$ is analyzed and compared with the Korteweg–de Vries equation $u_t+u_{xxx}-6uu_x=0$. Some integrals of motion for this equation are presented. The conditions are established under which a traveling wave is a solution to this equation.

Key words: nonlinear Korteweg–de Vries equation, traveling-wave solutions, semiconductors with strong spatial dispersion.

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English version:
Computational Mathematics and Mathematical Physics, 2008, 48:5, 764–768

Bibliographic databases:

UDC: 519.634
Received: 29.10.2007

Citation: A. B. Alshin, M. O. Korpusov, E. V. Yushkov, “Traveling-wave solution to a nonlinear equation in semiconductors with strong spatial dispersion”, Zh. Vychisl. Mat. Mat. Fiz., 48:5 (2008), 808–812; Comput. Math. Math. Phys., 48:5 (2008), 764–768

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Biswas A., Kara A.H., “1-Soliton solution and conservation laws for nonlinear wave equation in semiconductors”, Appl. Math. Comput., 217:8 (2010), 4289–4292  crossref  mathscinet  zmath  isi  elib  scopus
    2. Yushkov E.V., “Existence and blow-up of solutions of a pseudoparabolic equation”, Differ. Equ., 47:2 (2011), 291–295  crossref  mathscinet  zmath  isi  elib  elib  scopus
    3. E. V. Yushkov, “Blowup of solutions of a Korteweg–de Vries-type equation”, Theoret. and Math. Phys., 172:1 (2012), 932–938  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    4. Korpusov M.O., Yushkov E.V., “Local Solvability and Blow-Up For Benjamin-Bona-Mahony-Burgers, Rosenau-Burgers and Korteweg-de Vries-Benjamin-Bona-Mahony Equations”, Electron. J. Differ. Equ., 2014, 69  mathscinet  zmath  isi  elib
    5. A. I. Aristov, “On exact solutions of a nonclassical partial differential equation”, Comput. Math. Math. Phys., 55:11 (2015), 1836–1841  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    6. Gao B., He Ch., “Symmetry Analysis, Bifurcation and Exact Solutions of Nonlinear Wave Equation in Semiconductors With Strong Spatial Dispersion”, Electron. J. Differ. Equ., 2017, 42  mathscinet  isi
    7. A. I. Aristov, “On a Nonlinear Third-Order Equation”, Math. Notes, 102:1 (2017), 3–11  mathnet  crossref  crossref  mathscinet  isi  elib
    8. A. A. Bykov, K. E. Ermakova, “Resheniya uravnenii nestatsionarnogo fronta reaktsii s vyrozhdennymi tochkami ravnovesiya”, Model. i analiz inform. sistem, 24:3 (2017), 309–321  mathnet  crossref  elib
    9. A. A. Bykov, K. E. Ermakova, “Exact solutions of equations of a nonstationary front with equilibrium points of a fractional order”, Comput. Math. Math. Phys., 58:12 (2018), 1977–1988  mathnet  crossref  crossref  isi  elib
    10. A. I. Aristov, “On exact solutions of the Oskolkov–Benjamin–Bona–Mahony–Burgers equation”, Comput. Math. Math. Phys., 58:11 (2018), 1792–1803  mathnet  crossref  crossref  isi  elib
    11. Bykov A.A., Ermakova K.E., “Exact Solutions of the Equations of a Nonstationary Front With Equilibrium Points of An Infinite Order of Degeneracy”, Mosc. Univ. Phys. Bull., 73:6 (2018), 583–591  crossref  isi
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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