Publications

  1. J. Lenells and G. Misiolek, Amari-Chentsov connections and their geodesics on homogeneous spaces of diffeomorphism groups, J. Math. Sci. 196 (2014), 144–151, arXiv:1210.5476.
  2. J. Lenells, The KdV equation on the half-line: The Dirichlet to Neumann map, J. Phys. A 46 (2013), 345203, arXiv:1306.2652.
  3. B. Khesin, G. Misiolek, J. Lenells, and S. C. Preston, Curvatures of Sobolev metrics on diffeomorphism groups, Pure Appl. Math. Q. 9 (2013), 291–332, arXiv:1109.1816.
  4. J. Greenwald, J. Lenells, V. H. Satheeshkumar, and A. Wang, Gravitational collapse in Horava-Lifshitz theory, Phys. Rev. D 88 (2013), 024044, arXiv:1304.1167, 21pp.
  5. J. Lenells and M. Wunsch, The Hunter-Saxton system and the geodesics on a pseudosphere, Comm. PDE 38 (2013), 860–881, arXiv:1201.5002.
  6. J. Lenells and M. Wunsch, On the weakly dissipative Camassa-Holm, Degasperis-Procesi, and Novikov equations, J. Diff. Eq. 255 (2013), 441–448, arXiv:1207.0968.
  7. J. Lenells, Spheres, Kähler geometry, and the two-component Hunter-Saxton equation, Proc. Roy. Soc. A 469 (2013), 20120726, arXiv:1108.2727.
  8. B. Khesin, J. Lenells, G. Misiolek, and S. C. Preston, Geometry of diffeomorphism groups, complete integrability and geometric statistics Geom. Funct. Anal. 23 (2013), 334–366, arXiv:1105.0643.
  9. A. S. Fokas, J. Lenells, and B. Pelloni, Boundary value problems for the elliptic sine-Gordon equation in a semi-strip, J. Nonlinear Sci. 23 (2013), 241–282, arXiv:0912.1758, 40pp. 
  10. R. M. Chen, J. Lenells, and Y. Liu, Stability of the μ-Camassa-Holm peakons, J. Nonlinear Sci. 23 (2013), 97–112, arXiv:1011.4130.
  11. J. Lenells, The Degasperis-Procesi equation on the half-line, Nonlinear Anal. 76  (2013), 122–139, arXiv:1204.5252.
  12. J. Lenells and Z. Yang, A two-component geodesic equation on a space of constant positive curvature, J. Geom. Phys. 62 (2012), 1298–1308, arXiv:1109.2538.
  13. A. S. Fokas and J. Lenells, The unified method: I Non-linearizable problems on the half-line, J. Phys. A 45 (2012), 195201, arXiv:1109.4935.
  14. J. Lenells and A. S. Fokas, The unified method: II NLS on the half-line with t-periodic boundary conditions, J. Phys. A 45 (2012), 195202, arXiv:1109.4936.
  15. J. Lenells and A. S. Fokas, The unified method: III Non-linearizable problems on the interval, J. Phys. A 45 (2012), 195203, arXiv:1109.4937.
  16. J. Lenells, Initial-boundary value problems for integrable evolution equations with 3×3 Lax pairs, Physica D 241 (2012), 857–875, arXiv:1108.2875.
  17. J. Greenwald, J. Lenells, J. X. Lu, V. H. Satheeshkumar, and A. Wang, Black holes and global structures of spherical spacetimes in Horava-Lifshitz theory, Phys. Rev. D 84 (2011), 084040, 25 pp.
  18. J. Lenells and A. S. Fokas, Boundary value problems for the stationary axisymmetric Einstein equations: a rotating disc, Nonlinearity 24 (2011), 177-206.
  19. J. Lenells, Boundary value problems for the stationary axisymmetric Einstein equations: a disk rotating around a black hole, Comm. Math. Phys. 304 (2011), 585–635.
  20. J. Lenells, An integrable generalization of the sine-Gordon equation on the half-line, IMA J. Appl. Math. 76 (2011), 554–572.
  21. J. Lenells, The solution of the global relation for the derivative nonlinear Schrödinger equation on the half-line, Physica D 240 (2011), 512–525.
  22. J. Escher, M. Kohlmann, and J. Lenells, The geometry of the two-component Camassa-Holm and Degasperis-Procesi equations, J. Geom. Phys. 61 (2011), 436–452.
  23. J. Lenells, Dressing for a novel integrable generalization of the nonlinear Schrödinger equation, J. Nonlinear Sci. 20 (2010), 709–722.
  24. A. S. Fokas and J. Lenells, Explicit soliton asymptotics for the Korteweg-de Vries equation on the half-line, Nonlinearity 23 (2010), 937.
  25. J. Lenells, G. Misiolek, and F. Tiglay, Integrable evolution equations on spaces of tensor densitites and their peakon solutions, Commun. Math. Phys. 299 (2010), 129–161.
  26. J. Lenells and A. S. Fokas, On a novel integrable generalization of the sine-Gordon equation, J. Math. Phys. 51 (2010), 023519.
  27. A. Constantin, R. Ivanov, and J. Lenells, Inverse scattering transform for the Degasperis-Procesi equation, Nonlinearity 23 (2010), 2559–2575.
  28. J. Lenells and A. S. Fokas, An integrable generalization of the nonlinear Schrödinger equation on the half-line and solitons, Inverse problems, 25 (2009), 115006.
  29. J. Lenells, Exactly solvable model for nonlinear pulse propagation in optical fibers, Stud. Appl. Math. 123 (2009), 215–232.
  30. T. Dimofte, S. Gukov, J. Lenells, and D. Zagier, Exact results for perturbative Chern-Simons theory with complex gauge group, Commun. Number Theory Phys. 3 (2009), 1–81.
  31. J. Lenells and O. Lechtenfeld, On the N=2 supersymmetric Camassa-Holm and Hunter-Saxton equations, J. Math. Phys. 50 (2009), 012704.
  32. J. Lenells and A. S. Fokas, On a novel integrable generalization of the nonlinear Schrödinger equation, Nonlinearity 22 (2009), 11–27.
  33. J. Lenells, Periodic solitons of an equation for short capillary-gravity waves, J. Math. Anal. Appl. 352 (2009), 964–966.
  34. J. Lenells, The derivative nonlinear Schrödinger equation on the half-line, Physica D 237 (2008), 3008–3019.
  35. J. Lenells, A bi-Hamiltonian supersymmetric geodesic equation, Lett. Math. Phys. 85 (2008), 55–63.
  36. B. Khesin, J. Lenells, and G. Misiolek, Generalized Hunter-Saxton equation and the geometry of the group of circle diffeomorphisms, Math. Ann. 342 (2008), 617–656.
  37. J. Lenells, Poisson structure of a modified Hunter-Saxton equation, J. Phys. A: Math. Theor. 41 (2008), 285207.
  38. J. Lenells, The Hunter-Saxton equation: a geometric approach, SIAM J. Math. Anal. 40 (2008), 266–277.
  39. J. Lenells, Riemannian geometry on the diffeomorphism group of the circle, Ark. Mat. 45 (2007), 297–325.
  40. J. Lenells, The Hunter-Saxton equation describes the geodesic flow on a sphere, J. Geom. Phys. 57 (2007) 2049–2064.
  41. J. Lenells, Classification of all travelling-wave solutions for some nonlinear dispersive equations, Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 365 (2007),  2291–2298.
  42. J. Lenells, Weak geodesic flow and global solutions of the Hunter-Saxton equation, Discrete Contin. Dyn. Syst. 18 (2007),  643–656.
  43. J. Lenells, Infinite propagation speed of the Camassa-Holm equation, J. Math. Anal. Appl. 325 (2007), 1468–1478.
  44. J. Lenells, Classification of traveling waves for a class of nonlinear wave equations, J. Dyn. Diff. Eq. 18 (2006), 381–391.
  45. A. Constantin, B. Kolev, and J. Lenells, Integrability of invariant metrics on the Virasoro group, Phys. Lett. A 350 (2006), 75–80.
  46. J. Lenells, Traveling waves in compressible elastic rods, Disc. Cont. Dyn. Sys. B 6 (2006), 151–168.
  47. J. Lenells, Stability for the periodic Camassa-Holm equation, Math. Scand. 97 (2005), 188–200.
  48. J. Lenells, Traveling wave solutions of the Camassa-Holm equation, J. Diff. Eq. 217 (2005), 393–430.
  49. J. Lenells, Traveling wave solutions of the Degasperis-Procesi equation, J. Math. Anal. Appl. 306 (2005), 72–82.
  50. H. Kalisch and J. Lenells, Numerical study of traveling-wave solutions for the Camassa-Holm equation, Chaos, Solitons and Fractals 25 (2005), 287–298.
  51. J. Lenells, Conservation laws of the Camassa-Holm equation, J. Phys. A 38 (2005), 869–880.
  52. J. Lenells, The correspondence between KdV and Camassa-Holm, Int. Math. Res. Not. 71 (2004), 3797–3811.
  53. J. Lenells, Traveling wave solutions of the Camassa-Holm and Korteweg-de Vries equations, J. Nonlinear Math. Phys. 11 (2004), 508–520.
  54. J. Lenells, A variational approach to the stability of periodic peakons, J. Nonlinear Math. Phys. 11 (2004), 151–163.
  55. J. Lenells, Stability of periodic peakons, Internat. Math. Res. Notices 10 (2004), 485–499.
  56. A. Constantin and J. Lenells, On the inverse scattering approach for an integrable shallow water wave equation, Phys. Lett. A 308 (2003), 432–436.
  57. A. Constantin and J. Lenells, On the inverse scattering approach to the Camassa-Holm equation, J. Nonlinear Math. Phys. 10 (2003), 252–255.
  58. J. Lenells, The scattering approach for the Camassa-Holm equation, J. Nonlinear Math. Phys. 9 (2002), 389–393.
  59. J. Bengtsson, A. Hultgren, J. Lenells, and M. Lenells, Operator interface for a water tank process – a Java programming project, Proceedings of IFAC 99, Beijing, China, 1999.

Articles in Press

  1. A. S. Fokas and J. Lenells, The Unified Transform for the modified Helmholtz equation in the exterior of a square, in Unified Transform for Boundary Value Problems: Applications and Advances, A. S. Fokas and B. Pelloni (eds.), arXiv:1401.2502, 10pp.

ArXiv Preprints

  1. A. S. Fokas and J. Lenells, On the asymptotics of the Riemann zeta function to all orders, arXiv:1201.2633, 62pp.
  2. J. Lenells, Matrix Riemann-Hilbert problems with jumps across Carleson contours, arXiv:1401.2506, 34pp.
  3. A. S. Fokas and J. Lenells, Perturbative and exact results on the Neumann value for the nonlinear Schrödinger equation on the half-line, arXiv:1401.2508, 10pp.
  4. J. Lenells and A. S. Fokas, The nonlinear Schrödinger equation with t-periodic data: I. Exact results, arXiv:1412.0304, 22pp.
  5. J. Lenells and A. S. Fokas, The nonlinear Schrödinger equation with t-periodic data: II. Perturbative results, arXiv:1412.0306, 25pp.
  6. J. Lenells, Admissible boundary values for the defocusing nonlinear Schrödinger equation with asymptotically time-periodic data, arXiv:1407.5046, 21pp.
  7. J. Lenells, The defocusing nonlinear Schrödinger equation with t-periodic data: New exact solutions, arXiv:1412.3149, 25pp.
  8. J. Lenells, Absence of solitons for the defocusing NLS equation on the half-line, arXiv:1412.3495, 5pp.