Publications

20] Cavalcante, M.; Nascimento, A. C. On the propagation of regularity of solutions to the KdV equation on the positive half-line. Physica D: Nonlinear Phenomena, 484 (2025), 135030. DOI: 10.1016/j.physd.2025.135030.

[19] Cavalcante, M.; Marques, J. The Korteweg–de Vries equation on general star graphs. Zeitschrift für Angewandte Mathematik und Physik, 76 (2025), 230. DOI: 10.1007/s00033-025-02624-5.

[18] Angulo Pava, J.; Cavalcante, M. Dynamics of the Korteweg–de Vries equation on a balanced metric graph. Bulletin of the Brazilian Mathematical Society, New Series, 56 (2025), Article 5, 1–39. DOI: 10.1007/s00574-024-00429-0.

[17] Bárcena-Petisco, J. A.; Cavalcante, M.; Coclite, G. M.; De Nitti, N.; Zuazua, E. Control of hyperbolic and parabolic equations on networks and singular limits. Mathematical Control and Related Fields, 15 (2025), 348–389. DOI: 10.3934/mcrf.2024015.

[16] Cavalcante, M.; Huaroto, G. The cubic nonlinear fractional Schrödinger equation on the half-line. Nonlinear Analysis: Theory, Methods & Applications, 244 (2024), 113540. DOI: 10.1016/j.na.2024.113540.

[15] Cavalcante, M.; Muñoz, C. Asymptotic stability of KdV solitons on the half-line: A study in the energy space. SIAM Journal on Mathematical Analysis, 55 (2023), no. 5, 4337–4377. DOI: 10.1137/21M146377X.

[14] Capistrano-Filho, R. A.; Cavalcante, M.; Gallego, F. A. Controllability for Schrödinger type system with mixed dispersion on compact star graphs. Evolution Equations and Control Theory, 12 (2023), no. 1, 1–19. DOI: 10.3934/eect.2022019.

[13] Alejo, M. A.; Cavalcante, M.; Corcho, A. J. Stability of mKdV breathers on the half-line. Partial Differential Equations and Applications, 3 (2022), 70. DOI: 10.1007/s42985-022-00209-9.

[12] Capistrano-Filho, R. A.; Cavalcante, M.; Gallego, F. A. Forcing operators on star graphs applied for the cubic fourth order Schrödinger equation. Discrete and Continuous Dynamical Systems – Series B, 27 (2022), no. 6, 3399–3434. DOI: 10.3934/dcdsb.2021190.

[11] Angulo Pava, J.; Cavalcante, M. Linear instability criterion for the Korteweg–de Vries equation on metric star graphs. Nonlinearity, 34 (2021), no. 5, 3373–3410. DOI: 10.1088/1361-6544/abea6b.

[10] Capistrano-Filho, R. A.; Cavalcante, M. Stabilization and control for the biharmonic Schrödinger equation. Applied Mathematics & Optimization, 84 (2021), no. 1, 103–144. DOI: 10.1007/s00245-019-09640-8.

[9] Capistrano-Filho, R. A.; Cavalcante, M.; Gallego, F. A. Lower regularity solutions of the biharmonic Schrödinger equation in a quarter plane. Pacific Journal of Mathematics, 309 (2020), no. 1, 35–70. DOI: 10.2140/pjm.2020.309.35.

[8] Cavalcante, M.; Kwak, C. The initial-boundary value problem for the Kawahara equation on the half-line. Nonlinear Differential Equations and Applications, 27 (2020), 45. DOI: 10.1007/s00030-020-00648-6.

[7] Cavalcante, M.; Corcho, A. J. Well-posedness and lower bounds of the growth of weighted norms for the Schrödinger–Korteweg–de Vries interactions on the half-line. Journal of Evolution Equations, 20 (2020), 1563–1596. DOI: 10.1007/s00028-020-00566-1.

[6] Cavalcante, M. Initial boundary value problems for some nonlinear dispersive models on the half-line: A review and open problems. São Paulo Journal of Mathematical Sciences, 13 (2019), 418–434. DOI: 10.1007/s40863-019-00144-5.

[5] Cavalcante, M.; Muñoz, C. Stability of KdV solitons on the half-line. Revista Matemática Iberoamericana, 35 (2019), no. 6, 1809–1834. DOI: 10.4171/rmi/1102.

[4] Cavalcante, M.; Kwak, C. Local well-posedness of the fifth-order KdV-type equations on the half-line. Communications on Pure and Applied Analysis, 18 (2019), no. 5, 2607–2661. DOI: 10.3934/cpaa.2019117.

[3] Cavalcante, M.; Corcho, A. J. The initial-boundary value problem for the Schrödinger–Korteweg–de Vries system on the half-line. Communications in Contemporary Mathematics, 21 (2019), no. 8, 1850066. DOI: 10.1142/S0219199718500669.

[2] Cavalcante, M. The Korteweg–de Vries equation on a metric star graph. Zeitschrift für Angewandte Mathematik und Physik, 69 (2018), 124. DOI: 10.1007/s00033-018-1018-6.

[1] Cavalcante, M. The initial-boundary value problem for some quadratic nonlinear Schrödinger equations on the half-line. Differential and Integral Equations, 30 (2017), nos. 7–8, 521–554.