Research Publications of Mahendra Panthee


  1. J. L. Bona, H. Chen, Y. Hong, M. Panthee, M. Scialom; The effect of higher-order dissipation on solutions of the generalized Korteweg-de Vries equation. To appear in Communications in Contemporary Mathematics, 2024

  2. J. L. Bona, H. Chen, Y. Hong, M. Panthee, M. Scialom; The long wavelength limit of periodic solutions of water wave models. Studies in Applied Mathematics. 153:e12705. 2024. doi: 10.1111/sapm.12705

  3. Figueira, Renata O.; Nogueira, Marcelo; Panthee, Mahendra; Lower bounds on the radius of analyticity for a system of nonlinear quadratic interactions of the Schrödinger-type equations, Z. Angew. Math. Phys. 75 (2024), no. 4, Paper No. 136. doi: 10.1007/s00033-024-02279-8

  4.  Figueira, Renata O.; Panthee, Mahendra; Decay of the radius of spatial analyticity for the modified KdV equation and the nonlinear Schrödinger equation with third order dispersion. NoDEA Nonlinear Differential Equations Appl. 31 (2024), no. 4, Paper No. 68, 23 pp. doi: 10.1007/s00030-024-00960-5

  5.  Carvajal, X.; Panthee, M.; Sharp global well-posedness for the cubic nonlinear Schrödinger equation with third order dispersion. J. Fourier Anal. Appl. 30 (2024), no. 2, Paper No. 25, 23 pp. doi: 10.1007/s00041-024-10084-0

  6.  Figueira, Renata O.; Panthee, Mahendra; New lower bounds for the radius of analyticity for the mKdV equation and a system of mKdV-type equations. J. Evol. Equ. 24 (2024), no. 2, Paper No. 42, 24 pp. doi: 10.1007/s00028-024-00977-4

  7.  Corcho, Adán J.; Panthee, Mahendra; On the global and singular dynamics of the 2D cubic nonlinear Schrödinger equation on cylinders. Nonlinear Anal. 243 (2024), Paper No. 113519, 17 pp. doi: 10.1016/j.na.2024.113519

  8.  Baldasso, Mikaela; Panthee, Mahendra; Improved algebraic lower bound for the radius of spatial analyticity for the generalized KdV equation. Nonlinear Anal. Real World Appl. 77 (2024), Paper No. 104054, 11 pp.  doi: 10.1016/j.nonrwa.2023.104054

  9.  Figueira, Renata O.; Panthee, Mahendra; Evolution of the radius of analyticity for the generalized Benjamin equation. Discrete Contin. Dyn. Syst. 43 (2023), no. 8, 3043–3059. doi: 10.3934/dcds.2023039

  10.  Nogueira, Marcelo; Panthee, Mahendra; Local and global theory for the three-wave mixing Schrödinger system with quadratic interactions on Zoll manifolds. Anal. Math. Phys. 13 (2023), no. 1, Paper No. 7, 33 pp. doi: 10.1007/s13324-022-00766-7

  11. Carvajal, X.; Panthee, M.; Nonlinear Schrödinger equations with the third order dispersion on modulation spaces. Partial Differ. Equ. Appl. 3 (2022), no. 5, Paper No. 59, 21 pp. doi: 10.1007/s42985-022-00200-4

  12. Carvajal X.; Panthee M.; On propagation of regularities and evolution of radius of analyticity in the solution of the fifth-order KdV-BBM model. Z. Angew. Math. Phys. 73 (2022), no. 2, Paper No. 68, 15 pp

  13. Nogueira, Marcelo; Panthee, Mahendra; Local well-posedness for the quadratic Schrödinger equation in two-dimensional compact manifolds with boundary. São Paulo J. Math. Sci. 15 (2021), no. 2, 996–1024.

  14. Panthee M.; Vielma Leal F.; On the controllability and stabilization of the Benjamin equation on a periodic domain. Ann. Inst. H. Poincaré C Anal. Non Linéaire 38 (2021), no. 5, 1605–1652.

  15. Nogueira, Marcelo; Panthee, Mahendra; Local and global well-posedness for a quadratic Schrödinger system on Zoll manifolds. J. Math. Anal. Appl. 494 (2021), no. 1, Paper No. 124574, 36 pp.

  16. Carvajal, X.; Panthee, M.; Pastrán, R.; On the well-posedness, ill-posedness and norm-inflation for a higher order water wave model on a periodic domain. Nonlinear Anal. 192 (2020), 111713, 22 pp.

  17.  Nogueira, Marcelo; Panthee, Mahendra; On the Schrödinger-Debye system in compact Riemannian manifolds. Commun. Pure Appl. Anal. 19 (2020), no. 1, 425–453.

  18. Panthee, Mahendra; Vielma Leal, Francisco J.; On the controllability and stabilization of the linearized Benjamin equation on a periodic domain. Nonlinear Anal. Real World Appl. 51 (2020), 102978, 28 pp.

  19. Carvajal, Xavier; Panthee, Mahendra; Sharp well-posedness for a coupled system of mKdV-type equations. J. Evol. Equ. 19 (2019), no. 4, 1167–1197.

  20.  Carvajal, X.; Panthee, M.; On sharp global well-posedness and ill-posedness for a fifth-order KdV-BBM type equation. J. Math. Anal. Appl. 479 (2019), no. 1, 688–702.

  21. Linares, Felipe; Panthee, Mahendra; Robert, Tristan; Tzvetkov, Nikolay; On the periodic Zakharov-Kuznetsov equation. Discrete Contin. Dyn. Syst. 39 (2019), no. 6, 3521–3533.

  22.  Bhattarai, Santosh; Corcho, Adán J.; Panthee, Mahendra Well-posedness for multicomponent Schrödinger-gKdV systems and stability of solitary waves with prescribed mass. J. Dynam. Differential Equations 30 (2018), no. 2, 845–881.

  23. Bona, J. L.; Carvajal, X.; Panthee, M.; Scialom, M.; Higher-order Hamiltonian model for unidirectional water waves. J. Nonlinear Sci. 28 (2018), no. 2, 543–577.

  24. Carvajal, Xavier; Panthee, Mahendra; A note on local well-posedness of generalized KdV type equations with dissipative perturbations. From particle systems to partial differential equations, 85–100, Springer Proc. Math. Stat., 209, Springer, Cham, 2017.

  25. Carvajal, Xavier; Esfahani, Amin; Panthee, Mahendra; Well-posedness results and dissipative limit of high dimensional KdV-type equations. Bull. Braz. Math. Soc. (N.S.) 48 (2017), no. 4, 505–550. 

  26. Carvajal, Xavier; Panthee, Mahendra; Sharp local well-posedness of KdV type equations with dissipative perturbations, Quart. Appl. Math.74 (2016), no. 3, 571–594.

  27. Carvajal, X.; Panthee, M.; Scialom, M.; Comparison between model equations for long waves and blow-up phenomena, J. Math. Anal. Appl. 442 (2016), no. 1, 273–290.

  28. Carvajal, Xavier; Panthee, Mahendra; Scialom, Marcia; On well-posedness of the third-order nonlinear Schrödinger equation with time-dependent coefficients, Commun. Contemp. Math. 17 (2015), no. 4, 1450031, 24 pp.

  29. Carvajal, Xavier; Panthee, Mahendra; On ill-posedness for the generalized BBM equation, Discrete Contin. Dyn. Syst. 34 (2014), no. 11, 4565–4576.

  30. Panthee, Mahendra; Unique continuation property for the Benjamin equation, From particle systems to partial differential equations, 239–250, Springer Proc. Math. Stat., 75 Springer, Heidelberg, 2014.

  31. Carvajal, Xavier; Panthee, Mahendra; On the well-posedness of higher order viscous Burgers' equations, J. Math. Anal. Appl. 417 (2014), no. 1, 1–22.

  32. Panthee, M.; Scialom, M.; On the supercritical KdV equation with time-oscillating nonlinearity, NoDEA Nonlinear Differential Equations Appl. 20 (2013), no. 3, 1191–1212.

  33. Carvajal, X.; Gamboa, P.; Panthee, M.; A system of coupled Schrödinger equations with time-oscillating nonlinearity, Internat. J. Math. 23 (2012), no. 11, 1250119, 22 pp.

  34. Corcho, Adán J.; Panthee, Mahendra; Global well-posedness for a coupled modified KdV system, Bull. Braz. Math. Soc. (N.S.) 43 (2012), no. 1, 27–57.

  35. Carvajal, Xavier; Panthee, Mahendra ; Well-posedness of KdV type equations, Electron. J. Differential Equations 2012, No. 40, 15 pp.

  36. Carvajal, Xavier; Panthee, Mahendra; On uniqueness and decay of solution for Hirota equation, Appl. Math. Comput. 218 (2012), no. 9, 4928–4943.

  37. Gomes, Diogo A.; Panthee, Mahendra; Exponential energy decay for the Kadomtsev-Petviashvili (KP-II) equation, São Paulo J. Math. Sci. 5 (2011), no. 2, 135–148.

  38. Carvajal, X.; Panthee, M.; Scialom, M.; On the critical KDV equation with time-oscillating nonlinearity, Differential Integral Equations 24 (2011), no. 5-6, 541–567.

  39. Panthee, Mahendra; On the ill-posedness result for the BBM equation, Discrete Contin. Dyn. Syst. 30 (2011), no. 1, 253–259.

  40. Panthee, M.; Scialom, M.; Asymptotic behavior for a class of solutions to the critical modified Zakharov-Kuznetsov equation, Stud. Appl. Math. 124 (2010), no. 3, 229–245.

  41. Grünrock, Axel; Panthee, Mahendra; Drumond Silva, Jorge On KP-II type equations on cylinders. Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009), no. 6, 2335–2358.

  42. Panthee, M.; Scialom, M. On the Cauchy problem for a coupled system of KdV equations: critical case. Adv. Differential Equations 13 (2008), no. 1-2, 1–26.

  43. Carvajal, Xavier; Panthee, Mahendra; Well-posedness for some perturbations of the KdV equation with low regularity data, Electron. J. Differential Equations 2008, No. 02, 18 pp.

  44. Grünrock, Axel; Panthee, Mahendra; Silva, Jorge Drumond; A remark on global well-posedness below L2 for the GKDV-3 equation, Differential Integral Equations 20 (2007), no. 11, 1229–1236.

  45. Panthee, Mahendra; Silva, Jorge Drumond; Well-posedness for the Cauchy problem associated to the Hirota-Satsuma equation: periodic case, J. Math. Anal. Appl. 326 (2007), no. 2, 800–821.

  46. Panthee, Mahendra; Analytic solution for a system of KdV equations, Nepali Math. Sci. Rep. 26 (2006), no. 1-2, 47–54.

  47. Carvajal, X.; Panthee, M; On uniqueness of solution for a nonlinear Schrödinger-Airy equation, Nonlinear Anal. 64 (2006), no. 1, 146–158.

  48. Panthee, Mahendra; On the compact support of solutions to a nonlinear long internal waves model, Nepali Math. Sci. Rep. 24 (2005), no. 1, 49–58.

  49. Panthee, Mahendra; Unique continuation property for the Kadomtsev-Petviashvili (KP-II) equation, Electron. J. Differential Equations 2005, No. 59, 12 pp. (electronic).

  50. Carvajal, X.; Panthee, M; Unique continuation property for a higher order nonlinear Schrödinger equation, J. Math. Anal. Appl. 303 (2005), no. 1, 188–207.

  51. Linares, F.; Panthee, M; On the Cauchy problem for a coupled system of KdV equations, Commun. Pure Appl. Anal. 3 (2004), no. 3, 417–431.

  52. Panthee, Mahendra; A note on the unique continuation property for Zakharov-Kuznetsov equation, Nonlinear Anal. 59 (2004), no. 3, 425–438.