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Journal of Nonlinear Mathematical Physics Volume 15, 2008 - Issue sup3: Nonlinear Evolution Equations and Dynamical Systems 2007
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Original Articles

The Klein-Gordon Equation on the Half Line: a Riemann-Hilbert Approach

Beatrice Pelloni Department of Mathematics, University of Reading, Reading, RG6 6AX, UK E-mail: [email protected]@reading.ac.uk
&
Dimitrios A Pinotsis Department of Mathematics, University of Reading, Reading, RG6 6AX, UK E-mail: [email protected]@reading.ac.uk
Pages 334-336 | Published online: 21 Jan 2013

References

  • Ablowitz , M J , Kaur , D J , Newell , A C and Segur , H . 1973 . Method for solving the sine-Gordon equation . Phys. Rev. Lett. , 30 : 1262 – 1264 .
  • Fokas , A S . 1997 . A unified transform method for solving linear and certain nonlinear PDE's . Proc. Royal Soc. Series A , 453 : 1411 – 1443 .
  • Fokas , A S . 2001 . Two dimensional linear PDE’s in a convex polygon . Proc. Royal Soc. Lond. A , 457 : 371 – 393 .
  • Foxas , A S . 2004 . Linearizable initial-boundary value problems for the sine-Gordon equation on the half-line . Nonlinearity , 17 : 1521 – 1534 .
  • Foxas , A S . 2005 . The generalised Dirichlet to Neumann map for certain nonlinear evolution PDEs . Comm. Pure Appl. Math. , LVIII : 639 – 670 .
  • Foxas , A S and Gelfand , I M . 1994 . Integrability of linear and nonlinear evolution equations and the associated nonlinear Fourier transform . Lett. Math. Phys. , 3 : 189 – 210 .
  • Fokas , A S and Pelloni , B . 2007 . A generalised Dirichlet-to-Neumann map for evolutionary moving boundary value problems . J. Math. Phys. , 48 ( 1 ) 9 January : 189 – 210 . published online
  • Foxas , A S and Sung , L Y . 2005 . Generalized Fourier transforms, their nonlinearization and the imaging of the brain . Notices AMS , 52 : 1178 – 1192 .
  • Lax , P D . 1968 . Integrals of nonlinear evolution equations and solitary waves . Comm. Pur. Appl. Math. , 21 : 467 – 490 .
  • Pelloni , B . 2005 . The spectral representation oftwo-point boundary value problems for linear PDEs . Proc. Royal Soc. Lond. A , 461 : 2965 – 2984 .
  • Pelloni , B . 2005 . The asymptotic behaviour of the solution of boundary value problems for the sine-gordon equation on a finite interval . J. Nonlin. Math. Phys. , 12 ( 4 )
  • Pelloni , B . 2006 . Linear and nonlinear generalised Fourier transforms . Phil. Trans. Royal Soc. London , 364 : 3231 – 3249 .
  • Pinotsis , D A . 2007 . The Riemann-Hilbert formalism for certain linear and nonlinear integrable PDEs . J. Nonlin. Math. Phys. , 14 ( 3 ) : 466 – 485 .
  • Sklianin , E K . 1988 . Boundary conditions for integrabel quantum systems . J. Phys. A , 21 : 2375 – 2389 .

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