There is a specific class behind every ABAP WebDynpro component. This is generated by the system with category 80 - WebDynpro Runtime Object. You can view this class in SE24 only, and execute search within the class ( which is not provided in SE80 in WebDynpro Explorer) . You can search this way the usage of context nodes and their methods managing their data, or find a specific texts within a WebDynpro component. This report helps you do reach the corresponding class in one step. You can save the report under your local objects in SE80.
REPORT ZGETWDCOMPCLASS. DATA: gv_classname TYPE seoclsname. PARAMETERS p_wdcomp TYPE wdy_component_name. gv_classname = cl_wdy_wb_naming_service=>get_classname_for_component( p_wdcomp ). SET PARAMETER ID 'CLASS' FIELD gv_classname. CALL TRANSACTION 'SE24'.
After you've activated the report successfully, enter the WebDynpro Component name, and execute the report. It will navigate you to the Class Builder. Here just push buttom Display and start search with Ctrl+F or from the menu within the class. When you click double in the result list, the editor jumps to the method/section containing the text you looked for.
Info: Around NW 7.4, new option available in WD Browser, where you can switch to the code based controller display, and there you can use the search function to find a particular string in the source code.