Research Publications of Mahendra Panthee
J. L. Bona, H. Chen, Y. Hong, M. Panthee, M. Scialom; The long wavelength limit of periodic solutions of water wave models. To appear in Studies in Applied Mathematics. 2024.
R. O. Figueira, M. Panthee; Decay of the radius of spatial analyticity for the modified KdV equation and the nonlinear Schrödinger equation with third order dispersion. To appear in NODEA-Nonlinear Differential Equations and Applications, 2024.
X. Carvajal, M. Panthee; Sharp Global Well-Posedness for the Cubic Nonlinear Schrödinger Equation with Third Order Dispersion. Journal of Fourier Analysis and Applications, v. 30, p. 1-23, 2024. doi: 10.1007/s00041-024-10084-0
R. O. Figueira, M. Panthee; New lower bounds for the radius of analyticity for the mKdV equation and a system of mKdV-type equations. Journal of evolution Equations, v. 24, p. 1-24, 2024. doi: 10.1007/s00028-024-00977-4
A. J. Corcho, M. Panthee; On the global and singular dynamics of the 2D cubic nonlinear Schrödinger equation on cylinders. Nonlinear Analysis, TMA, v. 243, p. 113519, 2024. doi: 10.1016/j.na.2024.113519
M. Baldasso, M. Panthee, Improved algebraic lower bound for the radius of spatial analyticity for the generalized KdV equation, Nonlinear Anal. Real World Appl. 77 (2024), 104054. doi: 10.1016/j.nonrwa.2023.104054
R. O. Figueira, M. Panthee, Evolution of the radius of analyticity for the generalized Benjamin equation, Discrete Contin. Dyn. Syst. 43 (2023) 3043–3059. doi: 10.3934/dcds.2023039
M. Nogueira, M. Panthee; 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
Carvajal X., Panthee M.; Nonlinear schrödinger equations with the third order dispersion on modulation spaces. Partial Differential Equations and Applications, v. 3, p. 59, 2022. doi: 10.1007/s42985-022-00200-4
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
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.
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.
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.
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.
Nogueira, Marcelo; Panthee, Mahendra On the Schrödinger-Debye system in compact Riemannian manifolds. Commun. Pure Appl. Anal. 19 (2020), no. 1, 425–453.
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.
Carvajal, Xavier; Panthee, Mahendra Sharp well-posedness for a coupled system of mKdV-type equations. J. Evol. Equ. 19 (2019), no. 4, 1167–1197.
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.
Linares, Felipe; Panthee, Mahendra; Robert, Tristan; Tzvetkov, Nikolay On the periodic Zakharov-Kuznetsov equation. Discrete Contin. Dyn. Syst. 39 (2019), no. 6, 3521–3533.
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.
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.
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.
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.
Carvajal, Xavier; Panthee, Mahendra; Sharp local well-posedness of KdV type equations with dissipative perturbations, Quart. Appl. Math.74 (2016), no. 3, 571–594.
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.
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.
Carvajal, Xavier; Panthee, Mahendra; On ill-posedness for the generalized BBM equation, Discrete Contin. Dyn. Syst. 34 (2014), no. 11, 4565–4576.
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.
Carvajal, Xavier; Panthee, Mahendra; On the well-posedness of higher order viscous Burgers' equations, J. Math. Anal. Appl. 417 (2014), no. 1, 1–22.
Panthee, M.; Scialom, M.; On the supercritical KdV equation with time-oscillating nonlinearity, NoDEA Nonlinear Differential Equations Appl. 20 (2013), no. 3, 1191–1212.
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.
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.
Carvajal, Xavier; Panthee, Mahendra ; Well-posedness of KdV type equations, Electron. J. Differential Equations 2012, No. 40, 15 pp.
Carvajal, Xavier; Panthee, Mahendra; On uniqueness and decay of solution for Hirota equation, Appl. Math. Comput. 218 (2012), no. 9, 4928–4943.
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.
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.
Panthee, Mahendra; On the ill-posedness result for the BBM equation, Discrete Contin. Dyn. Syst. 30 (2011), no. 1, 253–259.
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.
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.
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.
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.
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.
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.
Panthee, Mahendra; Analytic solution for a system of KdV equations, Nepali Math. Sci. Rep. 26 (2006), no. 1-2, 47–54.
Carvajal, X.; Panthee, M; On uniqueness of solution for a nonlinear Schrödinger-Airy equation, Nonlinear Anal. 64 (2006), no. 1, 146–158.
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.
Panthee, Mahendra; Unique continuation property for the Kadomtsev-Petviashvili (KP-II) equation, Electron. J. Differential Equations 2005, No. 59, 12 pp. (electronic).
Carvajal, X.; Panthee, M; Unique continuation property for a higher order nonlinear Schrödinger equation, J. Math. Anal. Appl. 303 (2005), no. 1, 188–207.
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.
Panthee, Mahendra; A note on the unique continuation property for Zakharov-Kuznetsov equation, Nonlinear Anal. 59 (2004), no. 3, 425–438.