1. Complicated self-similar blow-up, compacton, and standing wave patterns for four nonlinear PDEs: a unified variational approach to elliptic equations -- 2. Classification of global sign-changing solutions of semilinear heat equations in the subcritical Fujita range: second- and higher-order diffusion -- 3. Global and blow-up solutions for Kuramoto-Sivashinsky, Navier-Stokes, and Burnett equations -- 4. Regional, single-point, and global blow-up for a fourth- order porous medium-type equation with source -- 5. Semilinear fourth-order hyperbolic equation: two types of blow-up patterns -- 6. Quasilinear fourth-order hyperbolic Boussinesq equation : shock, rarefaction, and fundamental solutions -- 7. Blow-up and global solutions for Korteweg-de Vries-type equations -- 8. Higher-order nonlinear dispersion PDEs : shock, rarefaction, and blow-up waves -- 9. Higher-order Schrodinger equations : fromblow-up zero structures to quasilinear operators.