Although advertising on internet dating website is not itself sufficient evidence of adultery, which is grounds for divorce under Jewish law, it would most probably amount to ‘ugly behaviour’ in the eyes of a rabbinical court. ‘Ugly behaviour’ is – in the eyes of Jewish law and the rabbinical court – negative behaviour on the wife’s part justifying grounds for divorce by the husband as it lays the seeds for adultery. Clearly if you have additional evidence – that she actually communicated and dated – rather than merely advertised over the internet, your case will be stronger.