A MULTIPLE SCALES METHOD FOR SOLVING NONLINEAR KdV7 EQUATION

Murat KOPARAN (Anadolu Üniversitesi, Eğitim Fakültesi, Matematik ve Fen Bilimleri Eğitimi Bölümü, Eskişehir, Türkiye)
Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi b- Teorik Bilimler
0 0
Yıl: 2018 Cilt: 6 Sayı: 2 Sayfa Aralığı: 140 - 153 Metin Dili: İngilizce DOI: 10.20290/aubtdb.349123 İndeks Tarihi: 07-01-2021

A MULTIPLE SCALES METHOD FOR SOLVING NONLINEAR KdV7 EQUATION

Öz:
In this report, a method of multiple scales is presented for the analysis of the (1+1)-dimensional seventh-order Korteweg-deVries (KdV7) equation and we derive nonlinear Schrödinger (NLS) type equation. Also we found the exact solutions for (1+1)-dimensional KdV7 equation by using the GGexpansion method. These methods are very simple and effective for gettingintegrability and exact solutions of KdV type equations.
Anahtar Kelime:

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
  • [1] Zakharov V, Kuznetsov E.A. Multiscale expansions in the theory of systems integrable by the inverse scattering transform. Physica D 1986; 18: 455-63.
  • [2] Calegora F, Degasperis A, Xiaosdo Ji. Nonlinear Schrödinger-type equations from multiscale reduction of PDEs I. Systematic derivation. J Math Phys 2001; 42: 2635-2652.
  • [3] Degasperis A, Manakov SV, Santini PM. Multiple-scale perturbation beyond nonlinear Schrödinger equation I. Physica D 1997; 100: 187-211.
  • [4] Osborne AR, Boffetta G. The shallow water NLS equation in Lagrangian coordinates. Phys Fluid A 1989; 1:1200-1210.
  • [5] Osborne AR, Boffetta G. A. Summable multiscale expansion for the KdV equation. In: Degasperis A, Fordy AP, Lakshmanan M, editors. Nonlinear evolution equations. Integrability and spectral Methods. MUP, Manchester and New York, 1991 pp. 559-571.
  • [6] Ozer MN, Dag I. The famous NLS equation from fifth-order integrable nonlinear evolution equations. Hadronic J 2001; 2: 195-206.
  • [7] Jafari H, Kadkhoda N, Biswas A. The   GG -expansion method for solutions of evolution equations from isothermal magneto static atmospheres, Journal of King Saud University-Science 2013; 25: 57-62.
  • [8] Zhang S, Dong L, Ba J, Sun Y. The  GG -expansion method for nonlinear differential-difference equations. Physics Letters A 2009; 373: 905-910.
  • [9] Aslan I. Discrete exact solutions to some nonlinear differential-difference equations via the  GG- expansion method. Applied Mathematics and Computation 2009; 8: 3140-3147.
  • [10] Zhang J, Wei X, Lu Y. A generalized  GG -expansion method and its applications. Physics Letters A 2008; 372: 3653-3658.
  • [11] Wang ML, Li XZ, Zhang JL. The  GG -expansion method and traveling wave solutions of nonlinear evolution equations in mathematical physics. Physics Letters A 2008; 372: 417-423.
  • [12] Tang B, He Y, Wei L, Wang S. Variable-coefficient discrete  GG -expansion method for nonlinear differential--difference equations. Physics Letters A 2011; 375: 3355-3361.
  • [13] Ayhan B, Bekir A. The  GG -expansion method for the nonlinear lattice equations, Communications in Nonlinear Science and Numerical Simulation 2012; 17: 3490-3498.
  • [14] Geng X, Xue B. N-soliton and quasi-periodic solutions of the KdV6 equations, Applied Mathematics and Computation 2012; 219: 3504-3510.
  • [15] Zhang S, Tong JL, Wang W. A generalized  GG -expansion method for the mKdV equation with variable coefficients, Physics Letters A 2008; 372: 2254-2257.
  • [16] Ayhan B, Özer MN, Bekir A. Method of Multiple Scales and Travelling Wave Solutions for (2+1)- Dimensional KdV Type Nonlinear Evolution Equations, Z. Naturforsch 2016; 71(8): 703-713.
  • [17] Hereman W, Banerjee PP, Korpel A, Assanto AG, Immerzeele V, Meerpoel A. Exact solitary wave solutions of nonlinear evolution and wave equations using a direct algebraic method, J. Phys. A: Math. Gen 1986; 19: 607-628
  • [18] Bilge AH. Integrability of seventh-order KdV-like evolution equations using formal symmetries and perturbations of conserved densities, J. Math. Phys 1992; 33: 3025–3038.
  • [19] Gerdt VP. Computer algebra, symmetry analysis and integrability of nonlinear evolution equations, Int. J. Mod. Phys. C 1993; 4: 279–286.
  • [20] Lax PD. Integrals of nonlinear equations of evolution and solitary waves. Comm. Pure Appl. Math 1968; 21: 467-490.
  • [21] Çakır F. Solutions of Nonlinear Equations Using Multiscale Expansion Method, Ph.D. thesis, Eskişehir Osmangazi University 2017; 79p
APA KOPARAN M (2018). A MULTIPLE SCALES METHOD FOR SOLVING NONLINEAR KdV7 EQUATION. , 140 - 153. 10.20290/aubtdb.349123
Chicago KOPARAN Murat A MULTIPLE SCALES METHOD FOR SOLVING NONLINEAR KdV7 EQUATION. (2018): 140 - 153. 10.20290/aubtdb.349123
MLA KOPARAN Murat A MULTIPLE SCALES METHOD FOR SOLVING NONLINEAR KdV7 EQUATION. , 2018, ss.140 - 153. 10.20290/aubtdb.349123
AMA KOPARAN M A MULTIPLE SCALES METHOD FOR SOLVING NONLINEAR KdV7 EQUATION. . 2018; 140 - 153. 10.20290/aubtdb.349123
Vancouver KOPARAN M A MULTIPLE SCALES METHOD FOR SOLVING NONLINEAR KdV7 EQUATION. . 2018; 140 - 153. 10.20290/aubtdb.349123
IEEE KOPARAN M "A MULTIPLE SCALES METHOD FOR SOLVING NONLINEAR KdV7 EQUATION." , ss.140 - 153, 2018. 10.20290/aubtdb.349123
ISNAD KOPARAN, Murat. "A MULTIPLE SCALES METHOD FOR SOLVING NONLINEAR KdV7 EQUATION". (2018), 140-153. https://doi.org/10.20290/aubtdb.349123
APA KOPARAN M (2018). A MULTIPLE SCALES METHOD FOR SOLVING NONLINEAR KdV7 EQUATION. Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi b- Teorik Bilimler, 6(2), 140 - 153. 10.20290/aubtdb.349123
Chicago KOPARAN Murat A MULTIPLE SCALES METHOD FOR SOLVING NONLINEAR KdV7 EQUATION. Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi b- Teorik Bilimler 6, no.2 (2018): 140 - 153. 10.20290/aubtdb.349123
MLA KOPARAN Murat A MULTIPLE SCALES METHOD FOR SOLVING NONLINEAR KdV7 EQUATION. Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi b- Teorik Bilimler, vol.6, no.2, 2018, ss.140 - 153. 10.20290/aubtdb.349123
AMA KOPARAN M A MULTIPLE SCALES METHOD FOR SOLVING NONLINEAR KdV7 EQUATION. Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi b- Teorik Bilimler. 2018; 6(2): 140 - 153. 10.20290/aubtdb.349123
Vancouver KOPARAN M A MULTIPLE SCALES METHOD FOR SOLVING NONLINEAR KdV7 EQUATION. Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi b- Teorik Bilimler. 2018; 6(2): 140 - 153. 10.20290/aubtdb.349123
IEEE KOPARAN M "A MULTIPLE SCALES METHOD FOR SOLVING NONLINEAR KdV7 EQUATION." Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi b- Teorik Bilimler, 6, ss.140 - 153, 2018. 10.20290/aubtdb.349123
ISNAD KOPARAN, Murat. "A MULTIPLE SCALES METHOD FOR SOLVING NONLINEAR KdV7 EQUATION". Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi b- Teorik Bilimler 6/2 (2018), 140-153. https://doi.org/10.20290/aubtdb.349123
Sayfa Oluşturulma Tarihi
17-04-2024 18:7

İLETİŞİM

TÜBİTAK ULAKBİM TR Dizin

Yüzüncüyıl, İşçi Blokları Mahallesi

Muhsin Yazıcıoğlu Caddesi No:51/C

06530 Çankaya / ANKARA +90 (312) 298 92 00

trdizin@tubitak.gov.tr

TÜBİTAK ULAKBİM Ulusal Akademik Ağ ve Bilgi Merkezi Cahit Arf Bilgi Merkezi © Tüm Hakları Saklıdır. Gizlilik Politikası Kullanım Şartları