Quick search Find article
Quick search
Find article

Geometrical optics in nonlinear media and integrable equations

FREE ARTICLE

Boris G Konopelchenko and Antonio Moro

Show affiliations


[1]
Zakharov V E, Manakov S V, Novikov S P and Pitaevski L P 1980 The Theory of Solitons: The Inverse Problem Method (Moscow: Nauka)

 
Zakharov V E, Manakov S V, Novikov S P and Pitaevski L P 1984 The Theory of Solitons: The Inverse Problem Method (New York: Plenum)

[2]
Ablowitz M J and Clarkson P 1991 Solitons, Nonlinear Evolution Equations and Inverse Scattering (Cambridge: Cambridge University Press)
CrossRef 
[3]
Jimbo M and Miwa T 1983 Publ. Res. Inst. Math. Sci., Kyoto Univ. 19 943
CrossRef 
[4]
Dijkgraaf R 1991 Intersection theory, integrable hierarchies and topological field theory New Symmetry Principles in Quantum Field Theory (NATO ASI) (Cargese 1991) (London: Plenum)

[5]
Konopelchenko B G 1992 Introduction to Multidimensional Integrable Equations (New York: Plenum)

[6]
Morozov A 1994 Phys.-Usp. 37 1

[7]
Di Francesco P, Ginsparg P and Zinn-Justin J 1995 Phys. Rep. 254 1

[8]
Shiota T 1986 Inven. Math. 83 333

[9]
Zakharov V E 1980 Funkt. Anal. Priloz. 14 89
CrossRef 
 
Zakharov V E 1981 Physica D 3 193
CrossRef 
[10]
Lax P D and Levermore C D 1983 Commun. Pure Appl. Math. 36 253
CrossRef 
 
Lax P D and Levermore C D 1983 Commun. Pure Appl. Math. 36 571
CrossRef 
 
Lax P D and Levermore C D 1983 Commun. Pure Appl. Math. 36 809
CrossRef 
[11]
Krichever I M 1988 Funkt. Anal. Priloz. 22 37

 
Krichever I M 1994 Commun. Pure. Appl. Math. 47 437
CrossRef 
 
Krichever I M 1992 Commun. Math. Phys. 143 415
CrossRef 
[12]
Kodama Y 1988 Phys. Lett. A 129 223
CrossRef 
 
Kodama Y 1990 Phys. Lett. A 147 477
CrossRef 
 
Aoyama S and Kodama Y 1996 Commun. Math. Phys. 182 185
CrossRef 
[13]
Dubrovin B A and Novikov S P 1989 Russ. Math. Surv. 44 35
IOPscience 
[14]
Takasaki K and Takebe T 1992 Int. J. Mod. Phys. A 1B 889
CrossRef 
 
Takasaki K and Takebe T 1995 Rev. Math. Phys. 7 743
CrossRef 
[15]
Ercolani N M et al (ed) 1994 Singular Limits of Dispersive Waves (NATO Adv. Sci. Inst. Ser. B Phys. vol 320) (New York: Plenum)

[16]
Dubrovin B A 1992 Commun. Math. Phys. 145 195
CrossRef 
 
Dubrovin B A 1992 Nucl. Phys. B 379 627
CrossRef 
 
Dubrovin B A and Zhang Y 1998 Commun. Math. Phys. 198 311
CrossRef 
[17]
Wiegmann P B and Zabrodin A 2000 Commun. Math. Phys. 213 523
CrossRef 
 
Mineev-Weinstein M, Wiegmann P B and Zabrodin A 2000 Phys. Rev. Lett. 84 5106
CrossRef  PubMed 
 
Krichever I, Mineev-Weinstein M, Wiegmanm P and Zabrodin A 2003 Laplacian growth and Whitham equations of soliton theory Preprint nlin. SI/0311005
Preprint 
[18]
Konopelchenko B and Martinez Alonso L 2001 Phys. Lett. A 286 161
CrossRef 
[19]
Konopelchenko B G and Martinez Alonso L 2002 J. Math. Phys. 43 3807
CrossRef 
[20]
Konopelchenko B G and Martinez Alonso L 2002 Stud. Appl. Math. 109 313
CrossRef 
[21]
Born M and Wolf E 1980 Principles of Optics (Oxford: Pergamon)

[22]
Cole K S and Cole R H 1941 J. Chem. Phys. 9 341
CrossRef 
[23]
Fannin P C 1996 J. Mol. Liq. 69 39
CrossRef 
 
Fannin P C and Charles S W 1995 J. Phys. D: Appl. Phys. 28 239
IOPscience 
[24]
Kimura Y, Hara S and Hayakawa R 2000 Phys. Rev. E 62 R5907
CrossRef 
[25]
Vekua I N 1962 Generalized Analytic Functions (Oxford: Pergamon)

[26]
Veselago V G 1968 Sov. Phys.-Usp. 10 509
IOPscience 
 
Shelby R A, Smith D R and Schultz S 2001 Science 292 77
CrossRef  PubMed 
[27]
Ahlfors L V 1966 Lectures on Quasi-Conformal Mappings (Princeton, NJ: Van Nostrand)

[28]
Letho O and Virtanen K I 1973 Quasi-Conformal Mappings in the Plane (Berlin: Springer)

crossref member

  1. Geometrical optics in nonlinear media and integrable equations

    Boris G Konopelchenko and Antonio Moro 2004 J. Phys. A: Math. Gen. 37 L105

  2. A distortion of pseudotetramers coupled with the Jahn–Teller effect in the geometrically frustrated spinel system CdV2O4

    Masashige Onoda and Junichi Hasegawa 2003 J. Phys.: Condens. Matter 15 L95

  3. Nanostructured chiral surfaces

    K-H Ernst et al 1999 Nanotechnology 10 355

  4. Waiting-Time Distributions in Lattice Models of Solar Flares

    James P. Norman et al. 2001 ApJ 557 891

  5. Transition from resonances to bound states in nonlinear systems: application to Bose–Einstein condensates

    Nimrod Moiseyev et al 2004 J. Phys. B: At. Mol. Opt. Phys. 37 L193

  6. Maximum entropy production and the fluctuation theorem

    R C Dewar 2005 J. Phys. A: Math. Gen. 38 L371

  7. Radio-astronomical Spectroscopy of the Hyperfine Structure of N2H+

    P. Caselli et al 1995 ApJ 455 L77

  8. The Proto-Planetary Nebula M1-92 and the Symbiotic Star MWC 560: Two Evolutionary Phases of the Same Type of Object?

    A. Arrieta et al. 2005 ApJ 623 252

  9. Categorization of quantum mechanics problems by professors and students

    Shih-Yin Lin and Chandralekha Singh 2010 Eur. J. Phys. 31 57

  10. Open Clusters as Galactic Disk Tracers. I. Project Motivation, Cluster Membership, and Bulk Three-Dimensional Kinematics

    Peter M. Frinchaboy and Steven R. Majewski 2008 The Astronomical Journal 136 118

Users also read

What's this?
This innovative new feature generates a list of articles 'also read' by other users based on them reading the original article. Article abstracts citations and references are all considered and weighted accordingly. We hope that this will help you find relevant papers for your research.

  1. The origin of power-law distributions in self-organized criticality
  2. Recursion operator for the stationary Nizhnik–Veselov–Novikov equation
  3. Leading off-diagonal approximation for the spectral form factor for uniformly hyperbolic systems
More

Related review articles

What's this?
View review articles related to this research to gain an insight into the key trends in this subject area. Related review articles are selected based on PACS/MSC codes, and are no more than three years old.

  1. Discrete breathers in Bose–Einstein condensates
  2. Anomalous current in periodic Lorentz gases with infinite horizon
  3. Optical tomography: forward and inverse problems
More

View by subject




Export








Please login to access our web services, or create an account if you don't yet have one.

You must have cookies enabled in your web browser to be able to login.

Username
Password

Forgotten your password? Get a new one here.